Theorem bj-notbid 10047

Description: Deduction form of bj-notbi 10045. (Contributed by BJ, 27-Jan-2020.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-notbid.1	⊢ (𝜑 → (𝜓 ↔ 𝜒))

Assertion

Ref	Expression
bj-notbid	⊢ (𝜑 → (¬ 𝜓 ↔ ¬ 𝜒))

Proof of Theorem bj-notbid

Step	Hyp	Ref	Expression
1		bj-notbid.1	. 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒))
2		bj-notbi 10045	. 2 ⊢ ((𝜓 ↔ 𝜒) → (¬ 𝜓 ↔ ¬ 𝜒))
3	1, 2	syl 14	1 ⊢ (𝜑 → (¬ 𝜓 ↔ ¬ 𝜒))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)