ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mp3anr3 GIF version

Theorem mp3anr3 1231
Description: An inference based on modus ponens. (Contributed by NM, 19-Oct-2007.)
Hypotheses
Ref Expression
mp3anr3.1 𝜃
mp3anr3.2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
mp3anr3 ((𝜑 ∧ (𝜓𝜒)) → 𝜏)

Proof of Theorem mp3anr3
StepHypRef Expression
1 mp3anr3.1 . . 3 𝜃
2 mp3anr3.2 . . . 4 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
32ancoms 255 . . 3 (((𝜓𝜒𝜃) ∧ 𝜑) → 𝜏)
41, 3mp3anl3 1228 . 2 (((𝜓𝜒) ∧ 𝜑) → 𝜏)
54ancoms 255 1 ((𝜑 ∧ (𝜓𝜒)) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator