Theorem bicon4i 401

Description: A contraposition inference.

Hypothesis

Ref	Expression
bicon4.1	⊢ (¬ φ ↔ ¬ ψ)

Assertion

Ref	Expression
bicon4i	⊢ (φ ↔ ψ)

Proof of Theorem bicon4i

Step	Hyp	Ref	Expression
1		bicon4.1	. 2 ⊢ (¬ φ ↔ ¬ ψ)
2		pm4.11 400	. 2 ⊢ ((φ ↔ ψ) ↔ (¬ φ ↔ ¬ ψ))
3	1, 2	mpbir 165	1 ⊢ (φ ↔ ψ)

Syntax hints:  ¬ wn 1   ↔ wb 127

This theorem is referenced by:  gencbval 1373  dfpss3 1558  eq0 1719  uni0b 1939  ltaddsub 4320

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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