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 Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantr2.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
adantrlr ((𝜑 ∧ ((𝜓𝜏) ∧ 𝜒)) → 𝜃)

Proof of Theorem adantrlr
StepHypRef Expression
1 simpl 472 . 2 ((𝜓𝜏) → 𝜓)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr1 682 1 ((𝜑 ∧ ((𝜓𝜏) ∧ 𝜒)) → 𝜃)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 196  df-an 385 This theorem is referenced by:  smoord  7349  addsrmo  9773  mulsrmo  9774  lediv12a  10795  nrmmetd  22189  pntrmax  25053  ablo4  26788  mdslmd3i  28575  atom1d  28596  esumiun  29483  poimirlem28  32607  fdc  32711  incsequz  32714  crngm4  32972  ps-2  33782  aacllem  42356
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