Theorem ancomst 465

Description: Closed form of ancoms 459. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

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

Proof of Theorem ancomst

Step	Hyp	Ref	Expression
1		ancom 461	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑))
2	1	imbi1i 350	1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒))

Syntax hints:   → wi 4   ↔ wb 207   ∧ wa 396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 208  df-an 397

This theorem is referenced by:  sbcom2  2183  ralcom  3267  ralcomf  3277  ovolgelb  25465  itg2leub  25719  nmoubi  30861  wl-sbcom2d  37932  ifpidg  43935  undmrnresiss  44048  ntrneiiso  44535  expcomdg  44944