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Metamath Proof Explorer

Theorem simp3l

Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011)

Ref Expression
Assertion simp3l ( ( 𝜑 ∧ 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 simpl ⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜒 )
2 1 3ad2ant3 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜒 )