Theorem ralel 3081

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 23	. 2 ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ 𝐴)
2	1	rgen 3080	1 ⊢ ∀𝑥 ∈ 𝐴 𝑥 ∈ 𝐴

This proof depends on syntax axioms:   ∈ wcel 2145  ∀wral 3078

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828

This proof depends on definitions:  df-bi 210  df-ral 3079

This theorem is used by:  raleleq  3333  rexuz3  15440  uvtx01vtx  29865  refrelcosslem  39308