Theorem ancomst 464

Description: Closed form of ancoms 458. (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 460	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑))
2	1	imbi1i 349	1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒))

Syntax hints:   → wi 4   ↔ wb 206   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  sbcom2  2178  ralcom  3264  ralcomf  3274  ovolgelb  25437  itg2leub  25691  nmoubi  30847  wl-sbcom2d  37762  ifpidg  43728  undmrnresiss  43841  ntrneiiso  44328  expcomdg  44737