Theorem dcan2 943

Description: A conjunction of two decidable propositions is decidable, expressed in a curried form as compared to dcan 942. 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 942	. 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 842

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 619  ax-in2 620  ax-io 717

This theorem depends on definitions:  df-bi 117  df-dc 843

This theorem is referenced by:  pcmptdvds  12981  1arith  13003  ctiunctlemudc  13121  nninfdclemp1  13134  lgsval  15806  lgscllem  15809  lgsneg  15826  lgsdir  15837  lgsdi  15839  lgsne0  15840  nninfsellemdc  16719