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	$$⊢\phi \to A\in B$$
Assertion	cardidd	$$⊢\phi \to \mathrm{card}\left(A\right)\approx A$$

Proof

Step	Hyp	Ref	Expression
1		cardidd.1	$$⊢\phi \to A\in B$$
2		cardidg	$$⊢A\in B\to \mathrm{card}\left(A\right)\approx A$$
3	1 2	syl	$$⊢\phi \to \mathrm{card}\left(A\right)\approx A$$