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Theorem adantlll 472
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 2-Dec-2012.)
Hypothesis
Ref Expression
adantl2.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
adantlll ((((𝜏𝜑) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem adantlll
StepHypRef Expression
1 simpr 109 . 2 ((𝜏𝜑) → 𝜑)
2 adantl2.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylanl1 400 1 ((((𝜏𝜑) ∧ 𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
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 is referenced by:  ad4ant23  507  ad4ant24  508  ad4ant234  1200  fun11iun  5435  fiintim  6873  cnegexlem3  8052  bezoutlemzz  11885  cnptopco  12622
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