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Theorem simp-4r 510
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)
Assertion
Ref Expression
simp-4r (((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Proof of Theorem simp-4r
StepHypRef Expression
1 simpllr 502 . 2 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜓)
21adantr 271 1 (((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  simp-5r  512  fimax2gtri  6671  finexdc  6672  exmidfodomrlemr  6889  exmidfodomrlemrALT  6890  supinfneg  9144  infsupneg  9145  hashunlem  10273  sumeq2  10809  fsumconst  10909
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