Theorem u2lemab 611

Description: Lemma for Dishkant implication study.

Assertion

Ref	Expression
u2lemab	((a ->2 b) ^ b) = b

Proof of Theorem u2lemab

Step	Hyp	Ref	Expression
1		df-i2 45	. . 3 (a ->2 b) = (b v (a' ^ b'))
2	1	ran 78	. 2 ((a ->2 b) ^ b) = ((b v (a' ^ b')) ^ b)
3		ancom 74	. . 3 ((b v (a' ^ b')) ^ b) = (b ^ (b v (a' ^ b')))
4		a5c 121	. . 3 (b ^ (b v (a' ^ b'))) = b
5	3, 4	ax-r2 36	. 2 ((b v (a' ^ b')) ^ b) = b
6	2, 5	ax-r2 36	1 ((a ->2 b) ^ b) = b

Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->2 wi2 13

This theorem is referenced by:  u2lemnonb 676  u21lembi 727  bi3 839  bi4 840

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  df-i2 45

Copyright terms: Public domain