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 → 𝐴 ∈ 𝐵 )
Assertion	cardidd	⊢ ( 𝜑 → ( card ‘ 𝐴 ) ≈ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		cardidd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝐵 )
2		cardidg	⊢ ( 𝐴 ∈ 𝐵 → ( card ‘ 𝐴 ) ≈ 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( card ‘ 𝐴 ) ≈ 𝐴 )