ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpd3an23 GIF version

Theorem mpd3an23 1245
Description: An inference based on modus ponens. (Contributed by NM, 4-Dec-2006.)
Hypotheses
Ref Expression
mpd3an23.1 (𝜑𝜓)
mpd3an23.2 (𝜑𝜒)
mpd3an23.3 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
mpd3an23 (𝜑𝜃)

Proof of Theorem mpd3an23
StepHypRef Expression
1 id 19 . 2 (𝜑𝜑)
2 mpd3an23.1 . 2 (𝜑𝜓)
3 mpd3an23.2 . 2 (𝜑𝜒)
4 mpd3an23.3 . 2 ((𝜑𝜓𝜒) → 𝜃)
51, 2, 3, 4syl3anc 1146 1 (𝜑𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  exp0  9424  bcpasc  9634  bccl  9635  pw2dvds  10254
  Copyright terms: Public domain W3C validator