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Theorem simp-4l 531
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)
Assertion
Ref Expression
simp-4l (((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Proof of Theorem simp-4l
StepHypRef Expression
1 simplll 523 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜑)
21adantr 274 1 (((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  simp-5l  533  disjiun  3930  fnfi  6831  sumeq2  11158  zsumdc  11183  modfsummod  11257  prodeq2  11356  cncnp  12431  fsumcncntop  12757  logbgcd1irrap  13088
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