ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ad4ant24 GIF version

Theorem ad4ant24 513
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
Hypothesis
Ref Expression
ad4ant2.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
ad4ant24 ((((𝜃𝜑) ∧ 𝜏) ∧ 𝜓) → 𝜒)

Proof of Theorem ad4ant24
StepHypRef Expression
1 ad4ant2.1 . . 3 ((𝜑𝜓) → 𝜒)
21adantlr 474 . 2 (((𝜑𝜏) ∧ 𝜓) → 𝜒)
32adantlll 477 1 ((((𝜃𝜑) ∧ 𝜏) ∧ 𝜓) → 𝜒)
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:  enwomnilem  7145
  Copyright terms: Public domain W3C validator