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Theorem ad5ant125 1360
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
ad5ant125 (((((𝜑𝜓) ∧ 𝜏) ∧ 𝜂) ∧ 𝜒) → 𝜃)

Proof of Theorem ad5ant125
StepHypRef Expression
1 ad5ant.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213expia 1115 . . 3 ((𝜑𝜓) → (𝜒𝜃))
322a1d 26 . 2 ((𝜑𝜓) → (𝜏 → (𝜂 → (𝜒𝜃))))
43imp41 428 1 (((((𝜑𝜓) ∧ 𝜏) ∧ 𝜂) ∧ 𝜒) → 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:  supxrge  41595  hoidmvlelem3  42869
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