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Theorem ad4ant234 1183
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
Hypothesis
Ref Expression
ad4ant3.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad4ant234 ((((𝜏𝜑) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem ad4ant234
StepHypRef Expression
1 ad4ant3.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expa 1111 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
32adantlll 697 1 ((((𝜏𝜑) ∧ 𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1071
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 383  df-3an 1073
This theorem is referenced by:  ad5ant234  1456  ad5ant235  1458
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