MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ad8antlr Structured version   Visualization version   GIF version

Theorem ad8antlr 772
Description: Deduction adding 8 conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017.)
Hypothesis
Ref Expression
ad2ant.1 (𝜑𝜓)
Assertion
Ref Expression
ad8antlr (((((((((𝜒𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓)

Proof of Theorem ad8antlr
StepHypRef Expression
1 ad2ant.1 . . 3 (𝜑𝜓)
21ad7antlr 770 . 2 ((((((((𝜒𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)
32adantr 479 1 (((((((((𝜒𝜑) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓)
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:  ad9antlr  774
  Copyright terms: Public domain W3C validator