Theorem u1lemnoa 642

Description: Lemma for Sasaki implication study.

Assertion

Ref	Expression
u1lemnoa	((a ->1 b)_|_ v a) = a

Proof of Theorem u1lemnoa

Step	Hyp	Ref	Expression
1		anor1 80	. . . 4 ((a ->1 b) ^ a_|_) = ((a ->1 b)_|_ v a)_|_
2	1	ax-r1 34	. . 3 ((a ->1 b)_|_ v a)_|_ = ((a ->1 b) ^ a_|_)
3		u1lemana 587	. . 3 ((a ->1 b) ^ a_|_) = a_|_
4	2, 3	ax-r2 35	. 2 ((a ->1 b)_|_ v a)_|_ = a_|_
5	4	con1 63	1 ((a ->1 b)_|_ v a) = a

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

This theorem is referenced by:  u1lem1 716

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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