Theorem con4bii 321

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 319	. 2 ⊢ ((𝜑 ↔ 𝜓) ↔ (¬ 𝜑 ↔ ¬ 𝜓))
3	1, 2	mpbir 231	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:  2false  375  equsexvw  2007  cbvexv1  2347  cbvex2v  2349  cbvex  2404  cbvex2  2417  rexcom  3267  cbvrexfw  3279  ceqsex  3491  ceqsexv  3492  gencbval  3503  ceqsralbv  3613  snnzb  4677  raldifsnb  4754  uni0b  4891  opab0  5510  tsna1  38392  ralopabb  43764