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Theorem simp-6l 787
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) (Proof shortened by Wolf Lammen, 24-May-2022.)
Assertion
Ref Expression
simp-6l (((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 𝜑)

Proof of Theorem simp-6l
StepHypRef Expression
1 id 22 . 2 (𝜑𝜑)
21ad6antr 736 1 (((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) → 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:  ghmcmn  19071  ustuqtop2  22994  ustuqtop4  22996  cnheibor  23707  miriso  26616  f1otrg  26817  txomap  31356  pstmxmet  31419  omssubadd  31837  signstfvneq0  32121  iunconnlem2  42093  suplesup  42416  limcleqr  42727  0ellimcdiv  42732  limclner  42734  fourierdlem51  43240  smflimlem2  43846
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