Theorem dcbii 826

Description: Equivalence property for decidability. Inference form. (Contributed by Jim Kingdon, 28-Mar-2018.)

Hypothesis

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

Assertion

Ref	Expression
dcbii	|- (DECID ph <-> DECID ps )

Proof of Theorem dcbii

Step	Hyp	Ref	Expression
1		dcbii.1	. 2 |- ( ph <-> ps )
2		dcbiit 825	. 2 |- ( ( ph <-> ps ) -> (DECID ph <-> DECID ps ) )
3	1, 2	ax-mp 5	1 |- (DECID ph <-> DECID ps )

Syntax hints:   <-> wb 104  DECID wdc 820

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116  df-dc 821

This theorem is referenced by:  dcbi  921  dcned  2333  dfrex2dc  2448  euxfr2dc  2897  exmidexmid  4156  pw1fin  6848  exfzdc  10121  fprod1p  11478  nninfsellemdc  13545