Theorem dcbiit 840

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 839	1 ⊢ ((𝜑 ↔ 𝜓) → (DECID 𝜑 ↔ DECID 𝜓))

Syntax hints:   → wi 4   ↔ wb 105  DECID wdc 835

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 710

This theorem depends on definitions:  df-bi 117  df-dc 836

This theorem is referenced by:  dcbii  841  bj-d0clsepcl  15571