Metamath Proof Explorer


Theorem simp1r1

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

Ref Expression
Assertion simp1r1 ( ( ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ) ∧ 𝜏𝜂 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simpr1 ( ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ) → 𝜑 )
2 1 3ad2ant1 ( ( ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ) ∧ 𝜏𝜂 ) → 𝜑 )