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 230	1 ⊢ (𝜑 ↔ 𝜓)

Syntax hints:  ¬ wn 3   ↔ wb 205

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 206

This theorem is referenced by:  2false  376  equsexvw  2008  cbvexv1  2339  cbvex2v  2342  cbvex  2399  cbvex2  2412  rexcom  3234  2ralorOLD  3297  cbvrexfw  3370  gencbval  3490  snnzb  4654  raldifsnb  4729  uni0b  4867  opab0  5467  ceqsralv2  33670  tsna1  36302