Metamath Proof Explorer


Theorem simpllr

Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009) (Proof shortened by Wolf Lammen, 6-Apr-2022)

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

Proof

Step Hyp Ref Expression
1 id ⊢ ( 𝜓 → 𝜓 )
2 1 ad3antlr ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜓 )