Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp-7r Structured version   Visualization version   GIF version

Theorem simp-7r 782
 Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) (Proof shortened by Wolf Lammen, 24-May-2022.)
Assertion
Ref Expression
simp-7r ((((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 𝜓)

Proof of Theorem simp-7r
StepHypRef Expression
1 simpr 471 . 2 ((𝜑𝜓) → 𝜓)
21ad6antr 720 1 ((((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 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 197  df-an 383 This theorem is referenced by:  simp-8rOLD  787  catass  16554  tgbtwnconn1  25691  legso  25715  miriso  25786  footex  25834  opphl  25867  lnopp2hpgb  25876  f1otrg  25972  2sqmo  29989  afsval  31089  smfmullem3  41517
 Copyright terms: Public domain W3C validator