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Theorem simp-5l 543
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)
Assertion
Ref Expression
simp-5l ((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜑)

Proof of Theorem simp-5l
StepHypRef Expression
1 simp-4l 541 . 2 (((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)
21adantr 276 1 ((((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem is referenced by:  simp-6l  545  xaddf  9828  nn0ltexp2  10671  xrmaxiflemlub  11237  dfgcd2  11995  ctiunctlemfo  12420  mhmmnd  12866  neitx  13428  limccnp2cntop  13806  limccoap  13807  lgsval  14065
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