Theorem bj-flddrng 37990

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 37989	. 2 ⊢ Field ⊆ DivRing
2	1	sseli 3934	1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2146  DivRingcdr 20877  Fieldcfield 20878

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 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-in 3913  df-ss 3923  df-field 20880

This theorem is used by: (None)