Metamath Proof Explorer
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 ) |