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Mirrors > Home > ILE Home > Th. List > eleqtrrdi | 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 2174 | . 2 ⊢ 𝐵 = 𝐶 |
4 | 1, 3 | eleqtrdi 2263 | 1 ⊢ (𝜑 → 𝐴 ∈ 𝐶) |
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