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Theorem adantrlr 754
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 471 . 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 382
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 195  df-an 384
This theorem is referenced by:  smoord  7326  addsrmo  9750  mulsrmo  9751  lediv12a  10767  nrmmetd  22136  pntrmax  24997  ablo4  26581  mdslmd3i  28368  atom1d  28389  esumiun  29276  poimirlem28  32390  fdc  32494  incsequz  32497  crngm4  32755  ps-2  33565  aacllem  42298
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