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Theorem adantrlr 722
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 484 . 2 ((𝜓𝜏) → 𝜓)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr1 681 1 ((𝜑 ∧ ((𝜓𝜏) ∧ 𝜒)) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397
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 206  df-an 398
This theorem is referenced by:  smoord  8365  addsrmo  11068  mulsrmo  11069  lediv12a  12107  nrmmetd  24083  pntrmax  27067  ablo4  29803  mdslmd3i  31585  atom1d  31606  fsumiunle  32035  esumiun  33092  poimirlem28  36516  fdc  36613  incsequz  36616  crngm4  36871  ps-2  38349  aacllem  47848
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