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Theorem adantrrl 715
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 477 . 2 ((𝜏𝜒) → 𝜒)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr2 673 1 ((𝜑 ∧ (𝜓 ∧ (𝜏𝜒))) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 198  df-an 385
This theorem is referenced by:  zorn2lem6  9576  ltmul12a  11133  mrcmndind  17634  neiint  21188  neissex  21211  1stcfb  21528  1stcrest  21536  grporcan  27764  mdslmd3i  29582  colineardim1  32544  cvratlem  35309  ps-2  35366
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