Theorem con2bid 319

Description: A contraposition deduction. (Contributed by NM, 15-Apr-1995.)

Hypothesis

Ref	Expression
con2bid.1	|- (ph -> (ps <-> -. ch))

Assertion

Ref	Expression
con2bid	|- (ph -> (ch <-> -. ps))

Proof of Theorem con2bid

Step	Hyp	Ref	Expression
1		con2bid.1	. 2 |- (ph -> (ps <-> -. ch))
2		con2bi 318	. 2 |- ((ch <-> -. ps) <-> (ps <-> -. ch))
3	1, 2	sylibr 203	1 |- (ph -> (ch <-> -. ps))

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:  con1bid  320  necon2abid  2574  necon2bbid  2575  r19.9rzv  3645  iotanul  4355