Theorem dcan2 937

Description: A conjunction of two decidable propositions is decidable, expressed in a curried form as compared to dcan 936. 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 936	. 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 836

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 615  ax-in2 616  ax-io 711

This theorem depends on definitions:  df-bi 117  df-dc 837

This theorem is referenced by:  pcmptdvds  12701  1arith  12723  ctiunctlemudc  12841  nninfdclemp1  12854  lgsval  15514  lgscllem  15517  lgsneg  15534  lgsdir  15545  lgsdi  15547  lgsne0  15548  nninfsellemdc  15984