Theorem pm4.1 143

Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116.

Assertion

Ref	Expression
pm4.1	⊢ ((φ → ψ) ↔ (¬ ψ → ¬ φ))

Proof of Theorem pm4.1

Step	Hyp	Ref	Expression
1		con3 86	. 2 ⊢ ((φ → ψ) → (¬ ψ → ¬ φ))
2		ax-3 5	. 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:  pm4.11 400  imbi1d 465  dfom2 2374  kmlem4 3583  indstr 4611

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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