Theorem ralel 3048

Description: All elements of a class are elements of the class. (Contributed by AV, 30-Oct-2020.)

Assertion

Ref	Expression
ralel	⊢ ∀𝑥 ∈ 𝐴 𝑥 ∈ 𝐴

Proof of Theorem ralel

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ 𝐴)
2	1	rgen 3047	1 ⊢ ∀𝑥 ∈ 𝐴 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2109  ∀wral 3045

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795

This theorem depends on definitions:  df-bi 207  df-ral 3046

This theorem is referenced by:  raleleq  3317  raleleqOLD  3318  rexuz3  15322  uvtx01vtx  29331  refrelcosslem  38460