Metamath Proof Explorer


Theorem simpr1

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

Ref Expression
Assertion simpr1 ( ( 𝜑 ∧ ( 𝜓𝜒𝜃 ) ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 simpr ( ( 𝜑𝜓 ) → 𝜓 )
2 1 3ad2antr1 ( ( 𝜑 ∧ ( 𝜓𝜒𝜃 ) ) → 𝜓 )