Theorem enrefg

Description: Equinumerosity is reflexive. Theorem 1 of Suppes p. 92. (Contributed by NM, 18-Jun-1998) (Revised by Mario Carneiro, 26-Apr-2015)

	Ref	Expression
Assertion	enrefg	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ≈ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		f1oi	⊢ ( I ↾ 𝐴 ) : 𝐴 –1-1-onto→ 𝐴
2		f1oen2g	⊢ ( ( 𝐴 ∈ 𝑉 ∧ 𝐴 ∈ 𝑉 ∧ ( I ↾ 𝐴 ) : 𝐴 –1-1-onto→ 𝐴 ) → 𝐴 ≈ 𝐴 )
3	1 2	mp3an3	⊢ ( ( 𝐴 ∈ 𝑉 ∧ 𝐴 ∈ 𝑉 ) → 𝐴 ≈ 𝐴 )
4	3	anidms	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ≈ 𝐴 )