Theorem con1biddc 888

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 885	. 2 |- (DECID ps -> ( ( -. ps <-> ch ) -> ( -. ch <-> ps ) ) )
3	1, 2	sylcom 28	1 |- ( ph -> (DECID ps -> ( -. ch <-> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 105  DECID wdc 846

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 623  ax-in2 624  ax-io 721

This theorem depends on definitions:  df-bi 117  df-stab 843  df-dc 847

This theorem is referenced by:  con2biddc  892  pm5.18dc  895  necon1abiddc  2482  necon1bbiddc  2483  eupth2lem3lem4fi  16628