Theorem ancomst 470

Description: Closed form of ancoms 464. (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 466	. 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑))
2	1	imbi1i 352	1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  sbcom2  2209  ralcom  3290  ralcomf  3300  ovolgelb  25708  itg2leub  25962  nmoubi  31253  wl-sbcom2d  38324  ifpidg  44331  undmrnresiss  44444  ntrneiiso  44931  expcomdg  45323