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Theorem ad5ant24 757
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
Hypothesis
Ref Expression
ad5ant2.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
ad5ant24 (((((𝜃𝜑) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant24
StepHypRef Expression
1 ad5ant2.1 . . 3 ((𝜑𝜓) → 𝜒)
21adantll 710 . 2 (((𝜃𝜑) ∧ 𝜓) → 𝜒)
32ad4ant13 747 1 (((((𝜃𝜑) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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
This theorem is referenced by:  omlimcl  8193  cofsmo  9679  leexp1a  13527  natpropd  17234  isucn2  22815  metust  23095  hpgerlem  26478  clwlkclwwlklem2a4  27702  cyc3genpm  30721  matunitlindflem1  34769  rexabslelem  41568
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