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| Mirrors > Home > MPE Home > Th. List > eleqtrrdi | Structured version Visualization version GIF version | ||
| Description: A membership and equality inference. (Contributed by NM, 24-Apr-2005.) |
| Ref | Expression |
|---|---|
| eleqtrrdi.1 | ⊢ (𝜑 → 𝐴 ∈ 𝐵) |
| eleqtrrdi.2 | ⊢ 𝐶 = 𝐵 |
| Ref | Expression |
|---|---|
| eleqtrrdi | ⊢ (𝜑 → 𝐴 ∈ 𝐶) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eleqtrrdi.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝐵) | |
| 2 | eleqtrrdi.2 | . . 3 ⊢ 𝐶 = 𝐵 | |
| 3 | 2 | eqcomi 2746 | . 2 ⊢ 𝐵 = 𝐶 |
| 4 | 1, 3 | eleqtrdi 2851 | 1 ⊢ (𝜑 → 𝐴 ∈ 𝐶) |
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