Theorem bj-notbii 10046

Description: Inference associated with bj-notbi 10045. (Contributed by BJ, 27-Jan-2020.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-notbii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
bj-notbii	⊢ (¬ 𝜑 ↔ ¬ 𝜓)

Proof of Theorem bj-notbii

Step	Hyp	Ref	Expression
1		bj-notbii.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		bj-notbi 10045	. 2 ⊢ ((𝜑 ↔ 𝜓) → (¬ 𝜑 ↔ ¬ 𝜓))
3	1, 2	ax-mp 7	1 ⊢ (¬ 𝜑 ↔ ¬ 𝜓)

Syntax hints:  ¬ wn 3   ↔ 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)