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Theorem simp3l1 1164
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3l1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)

Proof of Theorem simp3l1
StepHypRef Expression
1 simpl1 1062 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
213ad2ant3 1082 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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 197  df-an 386  df-3an 1038
This theorem is referenced by:  cvmlift2lem10  31037  noprefixmo  31608  cdleme26ee  35163  cdleme36m  35264  cdleme40m  35270  cdlemg18b  35482  cdlemk5u  35664  cdlemk6u  35665  cdlemk21N  35676  cdlemk20  35677  cdlemk27-3  35710  cdlemk28-3  35711  dihmeetlem20N  36130
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