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Theorem ad5ant135 1468
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
ad5ant135 (((((𝜑𝜏) ∧ 𝜓) ∧ 𝜂) ∧ 𝜒) → 𝜃)

Proof of Theorem ad5ant135
StepHypRef Expression
1 ad5ant.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
21ad4ant134 1181 . 2 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)
32adantlr 694 1 (((((𝜑𝜏) ∧ 𝜓) ∧ 𝜂) ∧ 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:  supxrgelem  40069  rexabslelem  40161  meaiuninc3v  41218  hoicvr  41282  hspmbllem2  41361  smfaddlem1  41491
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