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Theorem adantl6r 784
Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018.)
Hypothesis
Ref Expression
adantl6r.1 (((((((𝜑𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
Assertion
Ref Expression
adantl6r ((((((((𝜑𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)

Proof of Theorem adantl6r
StepHypRef Expression
1 adantl6r.1 . . . 4 (((((((𝜑𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅)
21ex 448 . . 3 ((((((𝜑𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆𝜅))
32adantl5r 783 . 2 (((((((𝜑𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆𝜅))
43imp 443 1 ((((((((𝜑𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 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:  pstmxmet  29061
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