Theorem con1biddc 770

Description: A contraposition deduction. (Contributed by Jim Kingdon, 4-Apr-2018.)

Hypothesis

Ref	Expression
con1biddc.1	|- ( ph -> (DECID ps -> ( -. ps <-> ch ) ) )

Assertion

Ref	Expression
con1biddc	|- ( ph -> (DECID ps -> ( -. ch <-> ps ) ) )

Proof of Theorem con1biddc

Step	Hyp	Ref	Expression
1		con1biddc.1	. 2 |- ( ph -> (DECID ps -> ( -. ps <-> ch ) ) )
2		con1biimdc 767	. 2 |- (DECID ps -> ( ( -. ps <-> ch ) -> ( -. ch <-> ps ) ) )
3	1, 2	sylcom 25	1 |- ( ph -> (DECID ps -> ( -. ch <-> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 98  DECID wdc 742

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 630

This theorem depends on definitions:  df-bi 110  df-dc 743

This theorem is referenced by:  con2biddc  774  pm5.18dc  777  necon1abiddc  2267  necon1bbiddc  2268