Theorem inv1 2303

Description: The intersection of a class with the universal class is itself. Exercise 4.10(k) of [Mendelson] p. 231.

Assertion

Ref	Expression
inv1	|- (A i^i V) = A

Proof of Theorem inv1

Step	Hyp	Ref	Expression
1		inss1 2233	. 2 |- (A i^i V) (_ A
2		ssid 2083	. . 3 |- A (_ A
3		ssv 2084	. . 3 |- A (_ V
4	2, 3	ssini 2236	. 2 |- A (_ (A i^i V)
5	1, 4	eqssi 2081	1 |- (A i^i V) = A

Syntax hints:   = wceq 958  Vcvv 1814   i^i cin 2049

This theorem is referenced by:  undif1 2344  onnev 3248  dmresv 3496  rescnvcnv 3499  curry1 4104  oev2 4168  cnfilca 10562

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-in 2054  df-ss 2056

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