Theorem con4bii 324

Description: A contraposition inference. (Contributed by NM, 21-May-1994.)

Hypothesis

Ref	Expression
con4bii.1	⊢ (¬ 𝜑 ↔ ¬ 𝜓)

Assertion

Ref	Expression
con4bii	⊢ (𝜑 ↔ 𝜓)

Proof of Theorem con4bii

Step	Hyp	Ref	Expression
1		con4bii.1	. 2 ⊢ (¬ 𝜑 ↔ ¬ 𝜓)
2		notbi 322	. 2 ⊢ ((𝜑 ↔ 𝜓) ↔ (¬ 𝜑 ↔ ¬ 𝜓))
3	1, 2	mpbir 234	1 ⊢ (𝜑 ↔ 𝜓)

Syntax hints:  ¬ wn 3   ↔ wb 209

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 210

This theorem is referenced by:  2false  378  equsexvw  2032  cbvexv1  2380  cbvex2v  2382  cbvex  2437  cbvex2  2450  rexcom  3300  cbvrexfw  3312  ceqsex  3510  ceqsexv  3511  gencbval  3521  ceqsralbv  3625  snnzb  4686  raldifsnb  4765  uni0b  4900  opab0  5537  tsna1  38678  ralopabb  44024