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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 1712 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | ax-8 1515 | . 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-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-gen 1460 ax-ie2 1505 ax-8 1515 ax-17 1537 ax-i9 1541 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: ax6evr 1716 equcom 1717 equcoms 1719 ax10 1728 cbv2h 1759 cbv2w 1761 equvini 1769 equveli 1770 equsb2 1797 drex1 1809 sbcof2 1821 aev 1823 cbvexdh 1938 rext 4233 iotaval 5207 prodmodc 11618 |
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