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Theorem simp331 1092
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp331 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)

Proof of Theorem simp331
StepHypRef Expression
1 simp31 975 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant3 962 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by: (None)
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