Theorem fnresin1 2735

Description: Restriction of a function's domain with an intersection.

Assertion

Ref	Expression
fnresin1	|- (F Fn A -> (F |` (A i^i B)) Fn (A i^i B))

Proof of Theorem fnresin1

Step	Hyp	Ref	Expression
1		inss1 1657	. 2 |- (A i^i B) (_ A
2		fnssres 2734	. 2 |- ((F Fn A /\ (A i^i B) (_ A) -> (F |` (A i^i B)) Fn (A i^i B))
3	1, 2	mpan2 519	1 |- (F Fn A -> (F |` (A i^i B)) Fn (A i^i B))

Syntax hints:   -> wi 2   i^i cin 1486   (_ wss 1487   |` cres 2412   Fn wfn 2417

This theorem is referenced by:  tfrlem5 2953

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-13 804  ax-14 805  ax-16 922  ax-17 925  ax-ext 1074  ax-rep 1075  ax-pow 1077

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-un 1490  df-in 1491  df-ss 1492  df-nul 1708  df-pw 1799  df-sn 1811  df-pr 1812  df-op 1815  df-br 2063  df-opab 2098  df-id 2125  df-xp 2424  df-rel 2425  df-cnv 2426  df-co 2427  df-dm 2428  df-res 2430  df-fun 2432  df-fn 2433

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