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Theorem adantl3r 782
Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018.)
Hypothesis
Ref Expression
adantl3r.1 ((((𝜑𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
Assertion
Ref Expression
adantl3r (((((𝜑𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Proof of Theorem adantl3r
StepHypRef Expression
1 adantl3r.1 . . . 4 ((((𝜑𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
21ex 449 . . 3 (((𝜑𝜌) ∧ 𝜇) → (𝜆𝜅))
32adantllr 751 . 2 ((((𝜑𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆𝜅))
43imp 444 1 (((((𝜑𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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 196  df-an 385
This theorem is referenced by:  adantl4r  783  ad5ant1345  1308  iscgrglt  25155  legov  25226  dfcgra2  25467  omssubadd  29483  poimirlem29  32402  adantlllr  38016  hspmbllem2  39311
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