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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 715 1 ((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1087
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 1089
This theorem is referenced by:  ad5ant124  1367  naddsuc2  8739  ixxin  13404  odf1  19580  m2cpmfo  22762  cnflf  24010  cnfcf  24050  tmdmulg  24100  blin  24431  blsscls2  24517  metcn  24556  xrsxmet  24831  sqf11  27182  dimval  33651  dfgcd3  37325  lindsadd  37620  hspmbllem2  46642
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