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Theorem simp-7l 807
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)
Assertion
Ref Expression
simp-7l ((((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 𝜑)

Proof of Theorem simp-7l
StepHypRef Expression
1 simp-6l 805 . 2 (((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜑)
21adantr 479 1 ((((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 𝜑)
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:  simp-8l  809  mhmmnd  17302  ustuqtop2  21794  0ellimcdiv  38516
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