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Theorem ad5ant245 1353
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
Hypothesis
Ref Expression
ad5ant.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad5ant245 (((((𝜏𝜑) ∧ 𝜂) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem ad5ant245
StepHypRef Expression
1 ad5ant.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213adant1l 1168 . 2 (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)
32ad4ant134 1166 1 (((((𝜏𝜑) ∧ 𝜂) ∧ 𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  2pthnloop  27439  matunitlindflem1  34769  nnfoctbdjlem  42614  sfprmdvdsmersenne  43645
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