Theorem lem3.3.3lem3 1050

Description: Lemma for lem3.3.3 1051.

Assertion

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

Proof of Theorem lem3.3.3lem3

Step	Hyp	Ref	Expression
1		lem3.3.3lem1 1048	. 2 (a ==5 b) =< (a ->1 b)
2		lem3.3.3lem2 1049	. 2 (a ==5 b) =< (b ->1 a)
3	1, 2	ler2an 173	1 (a ==5 b) =< ((a ->1 b) ^ (b ->1 a))

Syntax hints:   =< wle 2   ^ wa 7   ->1 wi1 12   ==5 wid5 22

This theorem is referenced by:  lem3.3.3 1051

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

Copyright terms: Public domain