Theorem dcan2 940

Description: A conjunction of two decidable propositions is decidable, expressed in a curried form as compared to dcan 939. This is deprecated; it's trivial to recreate with ex 115, but it's here in case someone is using this older form. (Contributed by Jim Kingdon, 12-Apr-2018.) (New usage is discouraged.)

Assertion

Ref	Expression
dcan2	|- (DECID ph -> (DECID ps -> DECID ( ph /\ ps ) ) )

Proof of Theorem dcan2

Step	Hyp	Ref	Expression
1		dcan 939	. 2 |- ( (DECID ph /\ DECID ps ) -> DECID ( ph /\ ps ) )
2	1	ex 115	1 |- (DECID ph -> (DECID ps -> DECID ( ph /\ ps ) ) )

Syntax hints:   -> wi 4   /\ wa 104  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:  pcmptdvds  12884  1arith  12906  ctiunctlemudc  13024  nninfdclemp1  13037  lgsval  15699  lgscllem  15702  lgsneg  15719  lgsdir  15730  lgsdi  15732  lgsne0  15733  nninfsellemdc  16464