Theorem bi2.03 144

Description: Contraposition. Bidirectional version of con2 82.

Assertion

Ref	Expression
bi2.03	⊢ ((φ → ¬ ψ) ↔ (ψ → ¬ φ))

Proof of Theorem bi2.03

Step	Hyp	Ref	Expression
1		con2 82	. 2 ⊢ ((φ → ¬ ψ) → (ψ → ¬ φ))
2		con2 82	. 2 ⊢ ((ψ → ¬ φ) → (φ → ¬ ψ))
3	1, 2	impbi 139	1 ⊢ ((φ → ¬ ψ) ↔ (ψ → ¬ φ))

Syntax hints:  ¬ wn 1   → wi 2   ↔ wb 127

This theorem is referenced by:  bicon2 403  ssconb 1598  oneqmini 2272

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

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