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Metamath Proof Explorer

Theorem simpl3

Description: Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009) (Proof shortened by Wolf Lammen, 23-Jun-2022)

Ref Expression
Assertion simpl3 ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 simpl ⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜒 )
2 1 3ad2antl3 ⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜒 )