Theorem con1b 323

Description: Contraposition. Bidirectional version of con1 120. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
con1b	|- ((-. ph -> ps) <-> (-. ps -> ph))

Proof of Theorem con1b

Step	Hyp	Ref	Expression
1		con1 120	. 2 |- ((-. ph -> ps) -> (-. ps -> ph))
2		con1 120	. 2 |- ((-. ps -> ph) -> (-. ph -> ps))
3	1, 2	impbii 180	1 |- ((-. ph -> ps) <-> (-. ps -> ph))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by: (None)