NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  mt4 GIF version

Theorem mt4 129
Description: The rule of modus tollens. (Contributed by Wolf Lammen, 12-May-2013.)
Hypotheses
Ref Expression
mt4.1 φ
mt4.2 ψ → ¬ φ)
Assertion
Ref Expression
mt4 ψ

Proof of Theorem mt4
StepHypRef Expression
1 mt4.1 . 2 φ
2 mt4.2 . . 3 ψ → ¬ φ)
32con4i 122 . 2 (φψ)
41, 3ax-mp 5 1 ψ
Colors of variables: wff setvar class
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: (None)
  Copyright terms: Public domain W3C validator