Theorem con1biidc 877

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

Hypothesis

Ref	Expression
con1biidc.1	|- (DECID ph -> ( -. ph <-> ps ) )

Assertion

Ref	Expression
con1biidc	|- (DECID ph -> ( -. ps <-> ph ) )

Proof of Theorem con1biidc

Step	Hyp	Ref	Expression
1		notnotbdc 872	. . 3 |- (DECID ph -> ( ph <-> -. -. ph ) )
2		con1biidc.1	. . . 4 |- (DECID ph -> ( -. ph <-> ps ) )
3	2	notbid 667	. . 3 |- (DECID ph -> ( -. -. ph <-> -. ps ) )
4	1, 3	bitrd 188	. 2 |- (DECID ph -> ( ph <-> -. ps ) )
5	4	bicomd 141	1 |- (DECID ph -> ( -. ps <-> ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 105  DECID wdc 834

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709

This theorem depends on definitions:  df-bi 117  df-dc 835

This theorem is referenced by:  con2biidc  879  necon1abiidc  2407  necon1bbiidc  2408