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Mirrors > Home > MPE Home > Th. List > equtr2OLD | Structured version Visualization version GIF version |
Description: Obsolete proof of equtr2 1941 as of 11-Apr-2021. (Contributed by NM, 12-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
equtr2OLD | ⊢ ((𝑥 = 𝑧 ∧ 𝑦 = 𝑧) → 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equtrr 1936 | . . 3 ⊢ (𝑧 = 𝑦 → (𝑥 = 𝑧 → 𝑥 = 𝑦)) | |
2 | 1 | equcoms 1934 | . 2 ⊢ (𝑦 = 𝑧 → (𝑥 = 𝑧 → 𝑥 = 𝑦)) |
3 | 2 | impcom 445 | 1 ⊢ ((𝑥 = 𝑧 ∧ 𝑦 = 𝑧) → 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 |
This theorem is referenced by: (None) |
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