Theorem bj-flddrng 35960

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 35959	. 2 ⊢ Field ⊆ DivRing
2	1	sseli 3973	1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing)

Syntax hints:   → wi 4   ∈ wcel 2106  DivRingcdr 20264  Fieldcfield 20265

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3474  df-in 3950  df-ss 3960  df-field 20267

This theorem is referenced by: (None)