Metamath Proof Explorer


Theorem ancomst

Description: Closed form of ancoms . (Contributed by Alan Sare, 31-Dec-2011)

Ref Expression
Assertion ancomst ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 ) )

Proof

Step Hyp Ref Expression
1 ancom ⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜓 ∧ 𝜑 ) )
2 1 imbi1i ⊢ ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜑 ) → 𝜒 ) )