Theorem bj-flddrng 38478

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 38477	. 2 ⊢ Field ⊆ DivRing
2	1	sseli 3909	1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2147  DivRingcdr 21031  Fieldcfield 21032

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-in 4094  df-field 21034

This theorem is used by: (None)