Theorem bi2.15 166

Description: Contraposition. Bidirectional version of con1 92.

Assertion

Ref	Expression
bi2.15	|- ((-. ph -> ps) <-> (-. ps -> ph))

Proof of Theorem bi2.15

Step	Hyp	Ref	Expression
1		con1 92	. 2 |- ((-. ph -> ps) -> (-. ps -> ph))
2		con1 92	. 2 |- ((-. ps -> ph) -> (-. ph -> ps))
3	1, 2	impbi 157	1 |- ((-. ph -> ps) <-> (-. ps -> ph))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146

This theorem is referenced by:  orcom 246  con2bi 525  dfbi3 670  pwssun 2827

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147

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