Theorem leoa 123

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

Hypothesis

Ref	Expression
leoa.1	(a v c) = b

Assertion

Ref	Expression
leoa	(a ^ b) = a

Proof of Theorem leoa

Step	Hyp	Ref	Expression
1		leoa.1	. . . 4 (a v c) = b
2	1	ax-r1 35	. . 3 b = (a v c)
3	2	lan 77	. 2 (a ^ b) = (a ^ (a v c))
4		a5c 121	. 2 (a ^ (a v c)) = a
5	3, 4	ax-r2 36	1 (a ^ b) = a

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

This theorem is referenced by:  df2le2 136  wlem3.1 210

This theorem was proved from axioms:  ax-a1 30  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

Copyright terms: Public domain