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Theorem adantlrl 473
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantl2.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
adantlrl (((𝜑 ∧ (𝜏𝜓)) ∧ 𝜒) → 𝜃)

Proof of Theorem adantlrl
StepHypRef Expression
1 simpr 109 . 2 ((𝜏𝜓) → 𝜓)
2 adantl2.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylanl2 400 1 (((𝜑 ∧ (𝜏𝜓)) ∧ 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:  mapxpen  6710  recexgt0sr  7549  fsumabs  11202  fsumiun  11214
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