Theorem u3lembi 723

Description: Kalmbach implication and biconditional. (Contributed by NM, 17-Jan-1998.)

Assertion

Ref	Expression
u3lembi	((a →3 b) ∩ (b →3 a)) = (a ≡ b)

Proof of Theorem u3lembi

Step	Hyp	Ref	Expression
1		i3bi 496	1 ((a →3 b) ∩ (b →3 a)) = (a ≡ b)

Syntax hints:   = wb 1   ≡ tb 5   ∩ wa 7   →₃ wi3 14

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by:  u3lemax4  796  u3lemax5  797