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Theorem 3adant3l 1142
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant3l ((𝜑𝜓 ∧ (𝜏𝜒)) → 𝜃)

Proof of Theorem 3adant3l
StepHypRef Expression
1 3adant1l.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213com13 1120 . . 3 ((𝜒𝜓𝜑) → 𝜃)
323adant1l 1138 . 2 (((𝜏𝜒) ∧ 𝜓𝜑) → 𝜃)
433com13 1120 1 ((𝜑𝜓 ∧ (𝜏𝜒)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  addassnqg  6538  mulassnqg  6540  prarloc  6659  prmuloc  6722  addasssrg  6899  axaddass  7004
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