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Theorem 3adant2l 1193
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant2l ((𝜑 ∧ (𝜏𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem 3adant2l
StepHypRef Expression
1 3adant1l.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213com12 1168 . . 3 ((𝜓𝜑𝜒) → 𝜃)
323adant1l 1191 . 2 (((𝜏𝜓) ∧ 𝜑𝜒) → 𝜃)
433com12 1168 1 ((𝜑 ∧ (𝜏𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 947
This theorem is referenced by:  sbthlemi4  6814  addassnqg  7154  mulassnqg  7156  prmuloc  7338  ltpopr  7367  addasssrg  7528  axaddass  7644
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