Theorem con1biidc 815

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 810	. . 3 |- (DECID ph -> ( ph <-> -. -. ph ) )
2		con1biidc.1	. . . 4 |- (DECID ph -> ( -. ph <-> ps ) )
3	2	notbid 633	. . 3 |- (DECID ph -> ( -. -. ph <-> -. ps ) )
4	1, 3	bitrd 187	. 2 |- (DECID ph -> ( ph <-> -. ps ) )
5	4	bicomd 140	1 |- (DECID ph -> ( -. ps <-> ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 104  DECID wdc 786

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 584  ax-in2 585  ax-io 671

This theorem depends on definitions:  df-bi 116  df-dc 787

This theorem is referenced by:  con2biidc  817  necon1abiidc  2327  necon1bbiidc  2328