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Theorem adantrrl 470
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 108 . 2 ((𝜏𝜒) → 𝜒)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr2 397 1 ((𝜑 ∧ (𝜓 ∧ (𝜏𝜒))) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem is referenced by:  1stconst  5873  ltexprlemdisj  6858  ltmul12a  8005
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