Theorem u1lemona 607

Description: Lemma for Sasaki implication study.

Assertion

Ref	Expression
u1lemona	((a ->1 b) v a_|_) = (a_|_ v (a ^ b))

Proof of Theorem u1lemona

Step	Hyp	Ref	Expression
1		df-i1 43	. . 3 (a ->1 b) = (a_|_ v (a ^ b))
2	1	ax-r5 37	. 2 ((a ->1 b) v a_|_) = ((a_|_ v (a ^ b)) v a_|_)
3		or32 75	. . 3 ((a_|_ v (a ^ b)) v a_|_) = ((a_|_ v a_|_) v (a ^ b))
4		oridm 102	. . . 4 (a_|_ v a_|_) = a_|_
5	4	ax-r5 37	. . 3 ((a_|_ v a_|_) v (a ^ b)) = (a_|_ v (a ^ b))
6	3, 5	ax-r2 35	. 2 ((a_|_ v (a ^ b)) v a_|_) = (a_|_ v (a ^ b))
7	2, 6	ax-r2 35	1 ((a ->1 b) v a_|_) = (a_|_ v (a ^ b))

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

This theorem is referenced by:  u1lemnaa 622  u1lem4 739

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-t 40  df-f 41  df-i1 43

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