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Metamath Proof Explorer

Theorem simp13r

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

Ref Expression
Assertion simp13r ( ( ( 𝜒 ∧ 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ) ∧ 𝜏 ∧ 𝜂 ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 simp3r ⊢ ( ( 𝜒 ∧ 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜓 )
2 1 3ad2ant1 ⊢ ( ( ( 𝜒 ∧ 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ) ∧ 𝜏 ∧ 𝜂 ) → 𝜓 )