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Theorem simp-7l 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-7l ((((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 𝜑)

Proof of Theorem simp-7l
StepHypRef Expression
1 id 22 . 2 (𝜑𝜑)
21ad7antr 738 1 ((((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399
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 210  df-an 400
This theorem is referenced by:  mhmmnd  18485  ustuqtop2  23140  cyc3genpm  31138  dimkerim  31422  0ellimcdiv  42865
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