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Theorem adantlllr 39721
Description: Deduction adding a conjunct to antecedent. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypothesis
Ref Expression
adantlllr.1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
adantlllr (((((𝜑𝜂) ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem adantlllr
StepHypRef Expression
1 adantlllr.1 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
21adantl3r 744 1 (((((𝜑𝜂) ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
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: (None)
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