Theorem dcbiit 851

Description: Equivalence property for decidability. Closed form. (Contributed by BJ, 27-Jan-2020.)

Assertion

Ref	Expression
dcbiit	⊢ ((𝜑 ↔ 𝜓) → (DECID 𝜑 ↔ DECID 𝜓))

Proof of Theorem dcbiit

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	dcbid 850	1 ⊢ ((𝜑 ↔ 𝜓) → (DECID 𝜑 ↔ DECID 𝜓))

This proof depends on syntax axioms:   → wi 4   ↔ wb 105  DECID wdc 846

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-io 721

This proof depends on definitions:  df-bi 117  df-dc 847

This theorem is used by:  dcbii  852  bj-d0clsepcl  16951