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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 1629 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | ax-8 1435 | . 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 104 ax-gen 1378 ax-ie2 1423 ax-8 1435 ax-17 1459 ax-i9 1463 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: equcom 1633 equcoms 1634 ax10 1645 cbv2h 1674 equvini 1681 equveli 1682 equsb2 1709 drex1 1719 sbcof2 1731 aev 1733 cbvexdh 1842 rext 3970 iotaval 4898 |
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