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Theorem 3adant1l 1166
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant1l (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)

Proof of Theorem 3adant1l
StepHypRef Expression
1 3adant1l.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213expb 1144 . . 3 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
32adantll 460 . 2 (((𝜏𝜑) ∧ (𝜓𝜒)) → 𝜃)
433impb 1139 1 (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 924
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 926
This theorem is referenced by:  3adant2l  1168  3adant3l  1170  tfrcl  6111  addassnqg  6920  mulassnqg  6922  addasssrg  7281  axaddass  7386
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