ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mpanl2 GIF version

Theorem mpanl2 431
Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Hypotheses
Ref Expression
mpanl2.1 𝜓
mpanl2.2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
mpanl2 ((𝜑𝜒) → 𝜃)

Proof of Theorem mpanl2
StepHypRef Expression
1 mpanl2.1 . . 3 𝜓
21jctr 313 . 2 (𝜑 → (𝜑𝜓))
3 mpanl2.2 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
42, 3sylan 281 1 ((𝜑𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  mpanr1  433  mp3an2  1288  reuss  3327  tfri3  6232  prarloclemarch2  7195  prarloclemlt  7269  prsradd  7562  map2psrprg  7581  pitonnlem2  7623  axcnre  7657  muleqadd  8396  divdivap2  8451  addltmul  8914
  Copyright terms: Public domain W3C validator