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Mirrors > Home > ILE Home > Th. List > eleqtrdi | GIF version |
Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006.) |
Ref | Expression |
---|---|
eleqtrdi.1 | ⊢ (𝜑 → 𝐴 ∈ 𝐵) |
eleqtrdi.2 | ⊢ 𝐵 = 𝐶 |
Ref | Expression |
---|---|
eleqtrdi | ⊢ (𝜑 → 𝐴 ∈ 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleqtrdi.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝐵) | |
2 | eleqtrdi.2 | . . 3 ⊢ 𝐵 = 𝐶 | |
3 | 2 | a1i 9 | . 2 ⊢ (𝜑 → 𝐵 = 𝐶) |
4 | 1, 3 | eleqtrd 2236 | 1 ⊢ (𝜑 → 𝐴 ∈ 𝐶) |
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