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	|- ( ph -> A e. B )
Assertion	cardidd	|- ( ph -> ( card ` A ) ~~ A )

Proof

Step	Hyp	Ref	Expression
1		cardidd.1	|- ( ph -> A e. B )
2		cardidg	|- ( A e. B -> ( card ` A ) ~~ A )
3	1 2	syl	|- ( ph -> ( card ` A ) ~~ A )