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Theorem adantrrl 756
 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
adantrrl ((𝜑 ∧ (𝜓 ∧ (𝜏𝜒))) → 𝜃)

Proof of Theorem adantrrl
StepHypRef Expression
1 simpr 476 . 2 ((𝜏𝜒) → 𝜒)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr2 683 1 ((𝜑 ∧ (𝜓 ∧ (𝜏𝜒))) → 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:  1stconst  7152  zorn2lem6  9206  ltmul12a  10758  mrcmndind  17189  neiint  20718  neissex  20741  1stcfb  21058  1stcrest  21066  grporcan  26756  mdslmd3i  28575  colineardim1  31338  cvratlem  33725  ps-2  33782
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