Theorem inv1 2299

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 2230	. 2 |- (A i^i V) (_ A
2		ssid 2080	. . 3 |- A (_ A
3		ssv 2081	. . 3 |- A (_ V
4	2, 3	ssini 2233	. 2 |- A (_ (A i^i V)
5	1, 4	eqssi 2078	1 |- (A i^i V) = A

Syntax hints:   = wceq 956  Vcvv 1811   i^i cin 2046

This theorem is referenced by:  undif1 2340  onnev 3242  dmresv 3490  rescnvcnv 3493  curry1 4098  oev2 4162  cnfilca 10583  cnfilcaOLD 10584

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-in 2051  df-ss 2053

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