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Theorem ad5ant134 1367
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
ad5ant134 (((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)

Proof of Theorem ad5ant134
StepHypRef Expression
1 ad5ant.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
21ad4ant134 1174 . 2 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)
32adantr 481 1 (((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1087
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 206  df-an 397  df-3an 1089
This theorem is referenced by:  qsidomlem1  32486  suplesup  43886  limsupvaluz2  44291  supcnvlimsup  44293  limsupgtlem  44330  xlimmnfvlem2  44386  xlimmnfv  44387  xlimpnfvlem2  44390  xlimpnfv  44391  sge0cl  44934  hspmbllem2  45180
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