Theorem con2biidc 847

Description: A contraposition inference. (Contributed by Jim Kingdon, 15-Mar-2018.)

Hypothesis

Ref	Expression
con2biidc.1	|- (DECID ps -> ( ph <-> -. ps ) )

Assertion

Ref	Expression
con2biidc	|- (DECID ps -> ( ps <-> -. ph ) )

Proof of Theorem con2biidc

Step	Hyp	Ref	Expression
1		con2biidc.1	. . . 4 |- (DECID ps -> ( ph <-> -. ps ) )
2	1	bicomd 140	. . 3 |- (DECID ps -> ( -. ps <-> ph ) )
3	2	con1biidc 845	. 2 |- (DECID ps -> ( -. ph <-> ps ) )
4	3	bicomd 140	1 |- (DECID ps -> ( ps <-> -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 104  DECID wdc 802

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681

This theorem depends on definitions:  df-bi 116  df-dc 803

This theorem is referenced by:  dfexdc  1460  nnedc  2287