Theorem con2bii2 38007

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 360	. 2 ⊢ (𝜓 ↔ ¬ 𝜑)
3	2	bicomi 227	1 ⊢ (¬ 𝜑 ↔ 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210

This theorem is used by:  fvineqsneq  38086