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Theorem adantlrr 467
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantl2.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
adantlrr (((𝜑 ∧ (𝜓𝜏)) ∧ 𝜒) → 𝜃)

Proof of Theorem adantlrr
StepHypRef Expression
1 simpl 107 . 2 ((𝜓𝜏) → 𝜓)
2 adantl2.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylanl2 395 1 (((𝜑 ∧ (𝜓𝜏)) ∧ 𝜒) → 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:  exmidfodomrlemim  6730  distrlem1prl  7044  distrlem1pru  7045  cnegex  7563  lcmgcdlem  10839  lcmdvds  10841
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