Theorem con1 146

Description: Contraposition. Theorem *2.15 of [WhiteheadRussell] p. 102. Its associated inference is con1i 147. (Contributed by NM, 29-Dec-1992.) (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 22	. 2 ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜑 → 𝜓))
2	1	con1d 145	1 ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜓 → 𝜑))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  con1b  358  nneob  8694  uzwo  12953