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Theorem mpanl2 419
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 302 . 2 (𝜑 → (𝜑𝜓))
3 mpanl2.2 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
42, 3sylan 271 1 ((𝜑𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
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 is referenced by:  mpanr1  421  mp3an2  1231  reuss  3245  tfri3  5983  prarloclemarch2  6574  prarloclemlt  6648  prsradd  6927  pitonnlem2  6980  axcnre  7012  muleqadd  7722  divdivap2  7774  addltmul  8217
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