Theorem con4bii 309

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 307	. 2 ⊢ ((𝜑 ↔ 𝜓) ↔ (¬ 𝜑 ↔ ¬ 𝜓))
3	1, 2	mpbir 219	1 ⊢ (𝜑 ↔ 𝜓)

Syntax hints:  ¬ wn 3   ↔ wb 194

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 195

This theorem is referenced by:  2false  363  2ralor  3083  gencbval  3220  snnzb  4193  raldifsnb  4261  uni0b  4389  ceqsralv2  30664  tsna1  32920