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Theorem ad4ant124 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
ad4ant124 ((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem ad4ant124
StepHypRef Expression
1 ad4ant3.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expa 1119 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
32adantlr 714 1 ((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  w3a 1088
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 206  df-an 398  df-3an 1090
This theorem is referenced by:  ad5ant124  1366  ixxin  13290  odf1  19352  m2cpmfo  22128  cnflf  23376  cnfcf  23416  tmdmulg  23466  blin  23797  blsscls2  23883  metcn  23922  xrsxmet  24195  sqf11  26511  dimval  32362  dfgcd3  35845  lindsadd  36121  naddsuc2  41756  hspmbllem2  44958
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