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Theorem ad4ant134 1287
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad4ant134.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad4ant134 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem ad4ant134
StepHypRef Expression
1 ad4ant134.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213exp 1255 . . 3 (𝜑 → (𝜓 → (𝜒𝜃)))
32a1d 25 . 2 (𝜑 → (𝜏 → (𝜓 → (𝜒𝜃))))
43imp41 616 1 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by:  ralxfrd2  4802  smflimlem4  39461  1wlkpwwlkf1ouspgr  41075  av-numclwlk1lem2foa  41520
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