Theorem con2biidc 891

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 141	. . 3 |- (DECID ps -> ( -. ps <-> ph ) )
3	2	con1biidc 889	. 2 |- (DECID ps -> ( -. ph <-> ps ) )
4	3	bicomd 141	1 |- (DECID ps -> ( ps <-> -. ph ) )

This proof depends on syntax axioms:   -. wn 3   -> wi 4   <-> wb 105  DECID wdc 846

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-io 721

This proof depends on definitions:  df-bi 117  df-dc 847

This theorem is used by:  dfexdc  1554  nnedc  2425