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Metamath Proof Explorer

Theorem cardidd

Description: Any set is equinumerous to its cardinal number. Deduction form of cardid . (Contributed by David Moews, 1-May-2017)

		Ref	Expression
	Hypothesis	cardidd.1	$⊢ φ \to A \in B$
	Assertion	cardidd	$⊢ φ \to card (A) \approx A$

Step	Hyp	Ref	Expression
1		cardidd.1	$⊢ φ \to A \in B$
2		cardidg	$⊢ A \in B \to card (A) \approx A$
3	1 2	syl	$⊢ φ \to card (A) \approx A$