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Theorem adantl4r 782
Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018.)
Hypothesis
Ref Expression
adantl4r.1 (((((𝜑𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
Assertion
Ref Expression
adantl4r ((((((𝜑𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Proof of Theorem adantl4r
StepHypRef Expression
1 adantl4r.1 . . . 4 (((((𝜑𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
21ex 448 . . 3 ((((𝜑𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆𝜅))
32adantl3r 781 . 2 (((((𝜑𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆𝜅))
43imp 443 1 ((((((𝜑𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
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 195  df-an 384
This theorem is referenced by:  adantl5r  783  perpneq  25327  pstmxmet  29074  icccncfext  38570  hspmbllem2  39314
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