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Theorem simp-8r 789
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) (Proof shortened by Wolf Lammen, 24-May-2022.)
Assertion
Ref Expression
simp-8r (((((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)

Proof of Theorem simp-8r
StepHypRef Expression
1 id 22 . 2 (𝜓𝜓)
21ad8antlr 738 1 (((((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395
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 206  df-an 396
This theorem is referenced by:  2sqmo  27284  legso  28284  opphl  28439  f1otrg  28556  2ndresdju  32308  cyc3conja  32753  mxidlprm  33027  mxidlirred  33029  qtophaus  33281  esumcst  33526  dffltz  41841  smfmullem3  45970
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