Theorem con3 126

Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-Feb-2013.)

Assertion

Ref	Expression
con3	⊢ ((φ → ψ) → (¬ ψ → ¬ φ))

Proof of Theorem con3

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((φ → ψ) → (φ → ψ))
2	1	con3d 125	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:  pm2.65  164  con34b  283  nic-ax  1438  nic-axALT  1439  exim  1575  hbnt  1775  nfndOLD  1792  hbimdOLD  1816  equsalhwOLD  1839  dvelimv  1939  ax9o  1950  ax11indn  2195  rexim  2719  ralf0  3657