MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ad5ant134 Structured version   Visualization version   GIF version

Theorem ad5ant134 1361
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 1168 . 2 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)
32adantr 483 1 (((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  w3a 1081
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 209  df-an 399  df-3an 1083
This theorem is referenced by:  qsidomlem1  30957  suplesup  41591  limsupvaluz2  42003  supcnvlimsup  42005  limsupgtlem  42042  xlimmnfvlem2  42098  xlimmnfv  42099  xlimpnfvlem2  42102  xlimpnfv  42103  sge0cl  42648  hspmbllem2  42894
  Copyright terms: Public domain W3C validator