Theorem u3lembi 705

Description: Kalmbach implication and biconditional.

Assertion

Ref	Expression
u3lembi	((a ->3 b) ^ (b ->3 a)) = (a == b)

Proof of Theorem u3lembi

Step	Hyp	Ref	Expression
1		i3bi 478	1 ((a ->3 b) ^ (b ->3 a)) = (a == b)

Syntax hints:   = wb 1   == tb 5   ^ wa 7   ->3 wi3 15

This theorem is referenced by:  u3lemax4 778  u3lemax5 779

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-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i3 45  df-le1 122  df-le2 123  df-c1 124  df-c2 125

metamath.org