Theorem con2bii2 37334

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

Hypothesis

Ref	Expression
con2bii2.1	⊢ (𝜑 ↔ ¬ 𝜓)

Assertion

Ref	Expression
con2bii2	⊢ (¬ 𝜑 ↔ 𝜓)

Proof of Theorem con2bii2

Step	Hyp	Ref	Expression
1		con2bii2.1	. . 3 ⊢ (𝜑 ↔ ¬ 𝜓)
2	1	con2bii 357	. 2 ⊢ (𝜓 ↔ ¬ 𝜑)
3	2	bicomi 224	1 ⊢ (¬ 𝜑 ↔ 𝜓)

Syntax hints:  ¬ wn 3   ↔ wb 206

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 207

This theorem is referenced by:  fvineqsneq  37413