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Mirrors > Home > MPE Home > Th. List > csbeq1a | Structured version Visualization version GIF version |
Description: Equality theorem for proper substitution into a class. (Contributed by NM, 10-Nov-2005.) |
Ref | Expression |
---|---|
csbeq1a | ⊢ (𝑥 = 𝐴 → 𝐵 = ⦋𝐴 / 𝑥⦌𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbid 3824 | . 2 ⊢ ⦋𝑥 / 𝑥⦌𝐵 = 𝐵 | |
2 | csbeq1 3814 | . 2 ⊢ (𝑥 = 𝐴 → ⦋𝑥 / 𝑥⦌𝐵 = ⦋𝐴 / 𝑥⦌𝐵) | |
3 | 1, 2 | eqtr3id 2792 | 1 ⊢ (𝑥 = 𝐴 → 𝐵 = ⦋𝐴 / 𝑥⦌𝐵) |
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