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Mirrors > Home > ILE Home > Th. List > equtr | GIF version |
Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.) |
Ref | Expression |
---|---|
equtr | ⊢ (𝑥 = 𝑦 → (𝑦 = 𝑧 → 𝑥 = 𝑧)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-8 1504 | . 2 ⊢ (𝑦 = 𝑥 → (𝑦 = 𝑧 → 𝑥 = 𝑧)) | |
2 | 1 | equcoms 1708 | 1 ⊢ (𝑥 = 𝑦 → (𝑦 = 𝑧 → 𝑥 = 𝑧)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-gen 1449 ax-ie2 1494 ax-8 1504 ax-17 1526 ax-i9 1530 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: equtrr 1710 equequ1 1712 equveli 1759 equvin 1863 |
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