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Theorem ad5ant124 1362
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
Hypothesis
Ref Expression
ad5ant.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad5ant124 (((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) ∧ 𝜂) → 𝜃)

Proof of Theorem ad5ant124
StepHypRef Expression
1 ad5ant.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
21ad4ant124 1170 . 2 ((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃)
32adantr 484 1 (((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) ∧ 𝜂) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1084
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 210  df-an 400  df-3an 1086
This theorem is referenced by:  xlimliminflimsup  42346  hspmbllem2  43108
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