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Theorem adantrll 693
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
adantrll ((𝜑 ∧ ((𝜏𝜓) ∧ 𝜒)) → 𝜃)

Proof of Theorem adantrll
StepHypRef Expression
1 simpr 471 . 2 ((𝜏𝜓) → 𝜓)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr1 653 1 ((𝜑 ∧ ((𝜏𝜓) ∧ 𝜒)) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 197  df-an 383
This theorem is referenced by:  lo1le  14589  nrmmetd  22598  mdslmd3i  29525
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