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 𝜑 → (DECID 𝜓 → DECID (𝜑 ∧ 𝜓)))

Proof of Theorem dcan2

Step	Hyp	Ref	Expression
1		dcan 936	. 2 ⊢ ((DECID 𝜑 ∧ DECID 𝜓) → DECID (𝜑 ∧ 𝜓))
2	1	ex 115	1 ⊢ (DECID 𝜑 → (DECID 𝜓 → DECID (𝜑 ∧ 𝜓)))

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  12738  1arith  12760  ctiunctlemudc  12878  nninfdclemp1  12891  lgsval  15551  lgscllem  15554  lgsneg  15571  lgsdir  15582  lgsdi  15584  lgsne0  15585  nninfsellemdc  16082