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Theorem ad4ant134 1174
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
ad4ant134 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem ad4ant134
StepHypRef Expression
1 ad4ant3.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expa 1118 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
32adantllr 719 1 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1086
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 207  df-an 396  df-3an 1088
This theorem is referenced by:  ad5ant245  1362  ad5ant134  1368  ad5ant135  1369  ad5ant145  1370  ralxfrd2  5411  gruwun  10854  lemul12b  12125  initoeu1  18057  termoeu1  18064  quscrng  21294  metss  24522  wlkswwlksf1o  29900  climxlim2lem  45865  smflimlem4  46794  isubgr3stgrlem8  47945
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