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Theorem ad4ant234 1172
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
Hypothesis
Ref Expression
ad4ant3.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad4ant234 ((((𝜏𝜑) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem ad4ant234
StepHypRef Expression
1 ad4ant3.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expa 1115 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
32adantlll 717 1 ((((𝜏𝜑) ∧ 𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1084
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 210  df-an 400  df-3an 1086
This theorem is referenced by:  ad5ant234  1359  ad5ant235  1360  xmulass  12668  decpmatmulsumfsupp  21376  pm2mpmhmlem1  21421  pm2mpmhmlem2  21422  clsnsg  22713
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