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Mirrors > Home > ILE Home > Th. List > equcomi | GIF version |
Description: Commutative law for equality. Lemma 7 of [Tarski] p. 69. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
equcomi | ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 1658 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | ax-8 1463 | . 2 ⊢ (𝑥 = 𝑦 → (𝑥 = 𝑥 → 𝑦 = 𝑥)) | |
3 | 1, 2 | mpi 15 | 1 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-gen 1406 ax-ie2 1451 ax-8 1463 ax-17 1487 ax-i9 1491 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: ax6evr 1662 equcom 1663 equcoms 1665 ax10 1676 cbv2h 1705 equvini 1712 equveli 1713 equsb2 1740 drex1 1750 sbcof2 1762 aev 1764 cbvexdh 1874 rext 4095 iotaval 5055 |
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