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Theorem adantl5r 763
Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018.)
Hypothesis
Ref Expression
adantl5r.1 ((((((𝜑𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
Assertion
Ref Expression
adantl5r (((((((𝜑𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Proof of Theorem adantl5r
StepHypRef Expression
1 adantl5r.1 . . . 4 ((((((𝜑𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
21ex 416 . . 3 (((((𝜑𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆𝜅))
32adantl4r 755 . 2 ((((((𝜑𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆𝜅))
43imp 410 1 (((((((𝜑𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399
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 210  df-an 400
This theorem is referenced by:  adantl6r  764  2sqmo  26318  pstmxmet  31561
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