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| Mirrors > Home > MPE Home > Th. List > eleqtrri | Structured version Visualization version GIF version | ||
| Description: Substitution of equal classes into membership relation. (Contributed by NM, 15-Jul-1993.) |
| Ref | Expression |
|---|---|
| eleqtrri.1 | ⊢ 𝐴 ∈ 𝐵 |
| eleqtrri.2 | ⊢ 𝐶 = 𝐵 |
| Ref | Expression |
|---|---|
| eleqtrri | ⊢ 𝐴 ∈ 𝐶 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eleqtrri.1 | . 2 ⊢ 𝐴 ∈ 𝐵 | |
| 2 | eleqtrri.2 | . . 3 ⊢ 𝐶 = 𝐵 | |
| 3 | 2 | eqcomi 2746 | . 2 ⊢ 𝐵 = 𝐶 |
| 4 | 1, 3 | eleqtri 2839 | 1 ⊢ 𝐴 ∈ 𝐶 |
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