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Metamath Proof Explorer

Theorem numth3

Description: All sets are well-orderable under choice. (Contributed by Stefan O'Rear, 28-Feb-2015)

		Ref	Expression
	Assertion	numth3	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ∈ dom card )

Step	Hyp	Ref	Expression
1		elex	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ∈ V )
2		cardeqv	⊢ dom card = V
3	1 2	eleqtrrdi	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ∈ dom card )