Theorem leao 124

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 31	. . 3 (a v b) = (b v a)
2		leao.1	. . . . . 6 (c ^ b) = a
3	2	ax-r1 35	. . . . 5 a = (c ^ b)
4		ancom 74	. . . . . 6 (b ^ c) = (c ^ b)
5	4	ax-r1 35	. . . . 5 (c ^ b) = (b ^ c)
6	3, 5	ax-r2 36	. . . 4 a = (b ^ c)
7	6	lor 70	. . 3 (b v a) = (b v (b ^ c))
8	1, 7	ax-r2 36	. 2 (a v b) = (b v (b ^ c))
9		a5b 120	. 2 (b v (b ^ c)) = b
10	8, 9	ax-r2 36	1 (a v b) = b

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

This theorem is referenced by:  df2le1 135

This theorem was proved from axioms:  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40

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