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Metamath Proof Explorer

Theorem simprl

Description: Simplification of a conjunction. (Contributed by NM, 21-Mar-2007)

Ref Expression
Assertion simprl ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 id ⊢ ( 𝜓 → 𝜓 )
2 1 ad2antrl ⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜓 )