Theorem wl-ralel 34883

Description: All elements of a class are elements of the class. (Contributed by Wolf Lammen, 10-Jun-2023.)

Assertion

Ref	Expression
wl-ralel	⊢ ∀(𝑥 : 𝐴)𝑥 ∈ 𝐴

Distinct variable group:   𝑥,𝐴

Proof of Theorem wl-ralel

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ 𝐴)
2	1	wl-rgen 34880	1 ⊢ ∀(𝑥 : 𝐴)𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2113  ∀wl-ral 34869

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 1969  ax-7 2014  ax-8 2115  ax-11 2160

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1780  df-clel 2892  df-wl-ral 34874

This theorem is referenced by: (None)