Theorem bj-flddrng 35387

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 35386	. 2 ⊢ Field ⊆ DivRing
2	1	sseli 3913	1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing)

Syntax hints:   → wi 4   ∈ wcel 2108  DivRingcdr 19906  Fieldcfield 19907

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-field 19909

This theorem is referenced by: (None)