Theorem con1bid 529

Description: A contraposition deduction.

Hypothesis

Ref	Expression
con1bid.1	|- (ph -> (-. ps <-> ch))

Assertion

Ref	Expression
con1bid	|- (ph -> (-. ch <-> ps))

Proof of Theorem con1bid

Step	Hyp	Ref	Expression
1		con1bid.1	. . . 4 |- (ph -> (-. ps <-> ch))
2	1	bicomd 523	. . 3 |- (ph -> (ch <-> -. ps))
3	2	con2bid 528	. 2 |- (ph -> (ps <-> -. ch))
4	3	bicomd 523	1 |- (ph -> (-. ch <-> ps))

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

This theorem is referenced by:  necon1abid 1621  necon1bbid 1622  onmindif 3066  pjnorm2t 9667  atdmd 10320  atmd2 10322

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  df-an 225

Copyright terms: Public domain