Theorem ssres 2589

Description: Subclass theorem for restriction.

Assertion

Ref	Expression
ssres	|- (A (_ B -> (A |` C) (_ (B |` C))

Proof of Theorem ssres

Step	Hyp	Ref	Expression
1		ssrin 1661	. 2 |- (A (_ B -> (A i^i (C X. V)) (_ (B i^i (C X. V)))
2		df-res 2430	. 2 |- (A |` C) = (A i^i (C X. V))
3		df-res 2430	. 2 |- (B |` C) = (B i^i (C X. V))
4	1, 2, 3	3sstr4g 1541	1 |- (A (_ B -> (A |` C) (_ (B |` C))

Syntax hints:   -> wi 2  Vcvv 1348   i^i cin 1486   (_ wss 1487   X. cxp 2408   |` cres 2412

This theorem is referenced by:  imass1 2621

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-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-in 1491  df-ss 1492  df-res 2430

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