Theorem dcbiit 829

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 828	1 ⊢ ((𝜑 ↔ 𝜓) → (DECID 𝜑 ↔ DECID 𝜓))

Syntax hints:   → wi 4   ↔ wb 104  DECID wdc 824

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116  df-dc 825

This theorem is referenced by:  dcbii  830  bj-d0clsepcl  13807