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Metamath Proof Explorer

Theorem simp3ll

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012)

Ref Expression
Assertion simp3ll ( ( 𝜃 ∧ 𝜏 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ) → 𝜑 )

Proof

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