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 ( 𝜑𝐴𝐵 )
Assertion cardidd ( 𝜑 → ( card ‘ 𝐴 ) ≈ 𝐴 )

Proof

Step Hyp Ref Expression
1 cardidd.1 ( 𝜑𝐴𝐵 )
2 cardidg ( 𝐴𝐵 → ( card ‘ 𝐴 ) ≈ 𝐴 )
3 1 2 syl ( 𝜑 → ( card ‘ 𝐴 ) ≈ 𝐴 )