Theorem con2biidc 772

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 129	. . 3 |- (DECID ps -> (-. ps <-> ph))
3	2	con1biidc 770	. 2 |- (DECID ps -> (-. ph <-> ps))
4	3	bicomd 129	1 |- (DECID ps -> (ps <-> -. ph))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 98  DECID wdc 741

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629

This theorem depends on definitions:  df-bi 110  df-dc 742

This theorem is referenced by:  dfexdc  1387  nnedc  2208