Metamath Proof Explorer


Theorem simp3rl

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

Ref Expression
Assertion simp3rl ( ( 𝜃𝜏 ∧ ( 𝜒 ∧ ( 𝜑𝜓 ) ) ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simprl ( ( 𝜒 ∧ ( 𝜑𝜓 ) ) → 𝜑 )
2 1 3ad2ant3 ( ( 𝜃𝜏 ∧ ( 𝜒 ∧ ( 𝜑𝜓 ) ) ) → 𝜑 )