Theorem con4bii 288

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 286	. 2 ⊢ ((φ ↔ ψ) ↔ (¬ φ ↔ ¬ ψ))
3	1, 2	mpbir 200	1 ⊢ (φ ↔ ψ)

Syntax hints:  ¬ wn 3   ↔ wb 176

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 177

This theorem is referenced by:  2false  339  19.35  1600  2ralor  2780  gencbval  2903  eq0  3564  ab0  3569  uni0b  3916