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Mirrors > Home > MPE Home > Th. List > equtr | Structured version Visualization version 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 | ax7 2014 | . 2 ⊢ (𝑦 = 𝑥 → (𝑦 = 𝑧 → 𝑥 = 𝑧)) | |
2 | 1 | equcoms 2018 | 1 ⊢ (𝑥 = 𝑦 → (𝑦 = 𝑧 → 𝑥 = 𝑧)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 |
This theorem is referenced by: equtrr 2020 equequ1 2023 equvinva 2028 ax6e 2392 equvini 2469 equviniOLD 2470 sbequiOLD 2527 sbequiALT 2589 axprlem3 5316 |
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