Theorem bj-flddrng 37933

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 37932	. 2 ⊢ Field ⊆ DivRing
2	1	sseli 3933	1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing)

Syntax hints:   → wi 4   ∈ wcel 2143  DivRingcdr 20827  Fieldcfield 20828

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-in 3912  df-ss 3922  df-field 20830

This theorem is referenced by: (None)