Theorem con1bii2 32355

Description: A contraposition inference. (Contributed by ML, 18-Oct-2020.)

Hypothesis

Ref	Expression
con1bii2.1	⊢ (¬ 𝜑 ↔ 𝜓)

Assertion

Ref	Expression
con1bii2	⊢ (𝜑 ↔ ¬ 𝜓)

Proof of Theorem con1bii2

Step	Hyp	Ref	Expression
1		con1bii2.1	. . 3 ⊢ (¬ 𝜑 ↔ 𝜓)
2	1	con1bii 345	. 2 ⊢ (¬ 𝜓 ↔ 𝜑)
3	2	bicomi 213	1 ⊢ (𝜑 ↔ ¬ 𝜓)

Syntax hints:  ¬ wn 3   ↔ wb 195

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 196

This theorem is referenced by: (None)