Theorem lem3.3.3lem1 1048

Description: Lemma for lem3.3.3 1051.

Assertion

Ref	Expression
lem3.3.3lem1	(a ==5 b) =< (a ->1 b)

Proof of Theorem lem3.3.3lem1

Step	Hyp	Ref	Expression
1		ax-a2 31	. . 3 ((a ^ b) v (a' ^ b')) = ((a' ^ b') v (a ^ b))
2		lea 160	. . . 4 (a' ^ b') =< a'
3	2	leror 152	. . 3 ((a' ^ b') v (a ^ b)) =< (a' v (a ^ b))
4	1, 3	bltr 138	. 2 ((a ^ b) v (a' ^ b')) =< (a' v (a ^ b))
5		df-id5 1046	. 2 (a ==5 b) = ((a ^ b) v (a' ^ b'))
6		df-i1 44	. 2 (a ->1 b) = (a' v (a ^ b))
7	4, 5, 6	le3tr1 140	1 (a ==5 b) =< (a ->1 b)

Syntax hints:   =< wle 2  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12   ==5 wid5 22

This theorem is referenced by:  lem3.3.3lem3 1050

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44  df-le1 130  df-le2 131  df-id5 1046

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