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Theorem ad4ant14 505
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
ad4ant14 ((((𝜑𝜃) ∧ 𝜏) ∧ 𝜓) → 𝜒)

Proof of Theorem ad4ant14
StepHypRef Expression
1 ad4ant2.1 . . 3 ((𝜑𝜓) → 𝜒)
21adantlr 468 . 2 (((𝜑𝜃) ∧ 𝜓) → 𝜒)
32adantlr 468 1 ((((𝜑𝜃) ∧ 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:  ad5ant15  512  ad5ant25  515  prodmodclem2  11358  prodmodc  11359
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