Description: A chained equinumerosity inference. (Contributed by NM, 25-Sep-2004)
Ref | Expression | ||
---|---|---|---|
Hypotheses | entri.1 | ⊢ 𝐴 ≈ 𝐵 | |
entri.2 | ⊢ 𝐵 ≈ 𝐶 | ||
Assertion | entri | ⊢ 𝐴 ≈ 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | entri.1 | ⊢ 𝐴 ≈ 𝐵 | |
2 | entri.2 | ⊢ 𝐵 ≈ 𝐶 | |
3 | entr | ⊢ ( ( 𝐴 ≈ 𝐵 ∧ 𝐵 ≈ 𝐶 ) → 𝐴 ≈ 𝐶 ) | |
4 | 1 2 3 | mp2an | ⊢ 𝐴 ≈ 𝐶 |