Theorem wleoa 358

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

Hypothesis

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

Assertion

Ref	Expression
wleoa	((a ^ b) == a) = 1

Proof of Theorem wleoa

Step	Hyp	Ref	Expression
1		wleoa.1	. . . 4 ((a v c) == b) = 1
2	1	wr1 189	. . 3 (b == (a v c)) = 1
3	2	wlan 352	. 2 ((a ^ b) == (a ^ (a v c))) = 1
4		wa5c 193	. 2 ((a ^ (a v c)) == a) = 1
5	3, 4	wr2 353	1 ((a ^ b) == a) = 1

Syntax hints:   = wb 1   == tb 5   v wo 6   ^ wa 7  1wt 9

This theorem is referenced by:  wdf2le2 368

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-wom 343

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44  df-le1 122  df-le2 123

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