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Theorem 3adant3l 1168
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 1146 . . 3 ((𝜒𝜓𝜑) → 𝜃)
323adant1l 1164 . 2 (((𝜏𝜒) ∧ 𝜓𝜑) → 𝜃)
433com13 1146 1 ((𝜑𝜓 ∧ (𝜏𝜒)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 924
This theorem is referenced by:  addassnqg  6885  mulassnqg  6887  prarloc  7006  prmuloc  7069  addasssrg  7246  axaddass  7351
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