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Theorem adantrrl 483
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 109 . 2 ((𝜏𝜒) → 𝜒)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr2 403 1 ((𝜑 ∧ (𝜓 ∧ (𝜏𝜒))) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  1stconst  6197  ltexprlemdisj  7555  axpre-suploclemres  7850  ltmul12a  8763  neiint  12898  neissex  12918
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