Theorem dcbii 845

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 844	. 2 |- ( ( ph <-> ps ) -> (DECID ph <-> DECID ps ) )
3	1, 2	ax-mp 5	1 |- (DECID ph <-> DECID ps )

Syntax hints:   <-> wb 105  DECID wdc 839

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 617  ax-in2 618  ax-io 714

This theorem depends on definitions:  df-bi 117  df-dc 840

This theorem is referenced by:  dcbi  942  dcned  2406  dfrex2dc  2521  euxfr2dc  2988  exmidexmid  4280  pw1fin  7072  tpfidceq  7092  dcfi  7148  elnn0dc  9806  elnndc  9807  exfzdc  10446  fprod1p  12110  bitsinv1  12473  nnwosdc  12560  prmdc  12652  pclemdc  12811  4sqlemafi  12918  4sqleminfi  12920  4sqexercise1  12921  nninfdclemcl  13019  nninfdclemp1  13021  psr1clfi  14652  nninfsellemdc  16376