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Theorem simp3l1 1069
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 967 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
213ad2ant3 987 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 945
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 depends on definitions:  df-bi 116  df-3an 947
This theorem is referenced by: (None)
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