Theorem bi2.15 145

Description: Contraposition. Bidirectional version of con1 84.

Assertion

Ref	Expression
bi2.15	⊢ ((¬ φ → ψ) ↔ (¬ ψ → φ))

Proof of Theorem bi2.15

Step	Hyp	Ref	Expression
1		con1 84	. 2 ⊢ ((¬ φ → ψ) → (¬ ψ → φ))
2		con1 84	. 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:  orcom 209  bicon2 403  dfbi 499  pwssun 1917

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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