Theorem resss 2587

Description: A class includes its restriction. Exercise 15 of [TakeutiZaring] p. 25.

Assertion

Ref	Expression
resss	|- (A |` B) (_ A

Proof of Theorem resss

Step	Hyp	Ref	Expression
1		df-res 2430	. 2 |- (A |` B) = (A i^i (B X. V))
2		inss1 1657	. 2 |- (A i^i (B X. V)) (_ A
3	1, 2	eqsstr 1530	1 |- (A |` B) (_ A

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

This theorem is referenced by:  relssres 2596  iss 2599  funres 2697  funres11 2709  funcnvres 2710  2elresin 2733  fssres 2764

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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