Theorem bj-flddrng 37284

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 37283	. 2 ⊢ Field ⊆ DivRing
2	1	sseli 3945	1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing)

Syntax hints:   → wi 4   ∈ wcel 2109  DivRingcdr 20645  Fieldcfield 20646

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-in 3924  df-ss 3934  df-field 20648

This theorem is referenced by: (None)