Theorem u5lem1 720

Description: Lemma for unified implication study.

Assertion

Ref	Expression
u5lem1	((a ->5 b) ->5 a) = ((a v b) ^ (a v b_|_))

Proof of Theorem u5lem1

Step	Hyp	Ref	Expression
1		u5lemc1 666	. . . 4 a C (a ->5 b)
2	1	comcom 435	. . 3 (a ->5 b) C a
3	2	u5lemc4 687	. 2 ((a ->5 b) ->5 a) = ((a ->5 b)_|_ v a)
4		u5lemnoa 646	. 2 ((a ->5 b)_|_ v a) = ((a v b) ^ (a v b_|_))
5	3, 4	ax-r2 35	1 ((a ->5 b) ->5 a) = ((a v b) ^ (a v b_|_))

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->5 wi5 17

This theorem is referenced by:  u5lem1n 725

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i5 47  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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