Theorem u1lemana 587

Description: Lemma for Sasaki implication study.

Assertion

Ref	Expression
u1lemana	((a ->1 b) ^ a_|_) = a_|_

Proof of Theorem u1lemana

Step	Hyp	Ref	Expression
1		df-i1 43	. . 3 (a ->1 b) = (a_|_ v (a ^ b))
2	1	ran 71	. 2 ((a ->1 b) ^ a_|_) = ((a_|_ v (a ^ b)) ^ a_|_)
3		ancom 68	. . 3 ((a_|_ v (a ^ b)) ^ a_|_) = (a_|_ ^ (a_|_ v (a ^ b)))
4		a5c 113	. . 3 (a_|_ ^ (a_|_ v (a ^ b))) = a_|_
5	3, 4	ax-r2 35	. 2 ((a_|_ v (a ^ b)) ^ a_|_) = a_|_
6	2, 5	ax-r2 35	1 ((a ->1 b) ^ a_|_) = a_|_

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->1 wi1 13

This theorem is referenced by:  u1lemnoa 642  u12lembi 708  u1lem7 754

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-i1 43

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