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Theorem ad5ant24 1223
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 693 . 2 (((𝜃𝜑) ∧ 𝜓) → 𝜒)
32ad4ant13 1206 1 (((((𝜃𝜑) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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
This theorem is referenced by:  metust  22583  clwlkclwwlklem2a4  27147  matunitlindflem1  33738  rexabslelem  40158
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