Theorem bj-flddrng 35460

Description: Fields are division rings (elemental version). (Contributed by BJ, 9-Nov-2024.)

Assertion

Ref	Expression
bj-flddrng	⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing)

Proof of Theorem bj-flddrng

Step	Hyp	Ref	Expression
1		bj-fldssdrng 35459	. 2 ⊢ Field ⊆ DivRing
2	1	sseli 3917	1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing)

Syntax hints:   → wi 4   ∈ wcel 2106  DivRingcdr 19991  Fieldcfield 19992

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ss 3904  df-field 19994

This theorem is referenced by: (None)