Theorem con4bii 288

Description: A contraposition inference. (Contributed by NM, 21-May-1994.)

Hypothesis

Ref	Expression
con4bii.1	|- (-. ph <-> -. ps)

Assertion

Ref	Expression
con4bii	|- (ph <-> ps)

Proof of Theorem con4bii

Step	Hyp	Ref	Expression
1		con4bii.1	. 2 |- (-. ph <-> -. ps)
2		notbi 286	. 2 |- ((ph <-> ps) <-> (-. ph <-> -. ps))
3	1, 2	mpbir 200	1 |- (ph <-> ps)

Syntax hints:  -. wn 3   <-> wb 176

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  2false  339  19.35  1600  2ralor  2781  gencbval  2904  eq0  3565  ab0  3570  uni0b  3917