Theorem bj-flddrng 38041

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 38040	. 2 ⊢ Field ⊆ DivRing
2	1	sseli 3927	1 ⊢ (𝐹 ∈ Field → 𝐹 ∈ DivRing)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2145  DivRingcdr 20890  Fieldcfield 20891

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 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-in 3906  df-ss 3916  df-field 20893

This theorem is used by: (None)