Theorem leao 116

Description: Relation between two methods of expressing "less than or equal to".

Hypothesis

Ref	Expression
leao.1	(c ^ b) = a

Assertion

Ref	Expression
leao	(a v b) = b

Proof of Theorem leao

Step	Hyp	Ref	Expression
1		ax-a2 30	. . 3 (a v b) = (b v a)
2		leao.1	. . . . . 6 (c ^ b) = a
3	2	ax-r1 34	. . . . 5 a = (c ^ b)
4		ancom 68	. . . . . 6 (b ^ c) = (c ^ b)
5	4	ax-r1 34	. . . . 5 (c ^ b) = (b ^ c)
6	3, 5	ax-r2 35	. . . 4 a = (b ^ c)
7	6	lor 66	. . 3 (b v a) = (b v (b ^ c))
8	1, 7	ax-r2 35	. 2 (a v b) = (b v (b ^ c))
9		a5b 112	. 2 (b v (b ^ c)) = b
10	8, 9	ax-r2 35	1 (a v b) = b

Syntax hints:   = wb 1   v wo 6   ^ wa 7

This theorem is referenced by:  df2le1 127

This theorem was proved from axioms:  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

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