Theorem con1 120

Description: Contraposition. Theorem *2.15 of [WhiteheadRussell] p. 102. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Feb-2013.)

Assertion

Ref	Expression
con1	⊢ ((¬ φ → ψ) → (¬ ψ → φ))

Proof of Theorem con1

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((¬ φ → ψ) → (¬ φ → ψ))
2	1	con1d 116	1 ⊢ ((¬ φ → ψ) → (¬ ψ → φ))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  con1b  323  ax12olem3  1929