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Mirrors > Home > ILE Home > Th. List > ax6evr | GIF version |
Description: A commuted form of a9ev 1684. The naming reflects how axioms were numbered in the Metamath Proof Explorer as of 2020 (a numbering which we eventually plan to adopt here too, but until this happens everywhere only some theorems will have it). (Contributed by BJ, 7-Dec-2020.) |
Ref | Expression |
---|---|
ax6evr | ⊢ ∃𝑥 𝑦 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9ev 1684 | . 2 ⊢ ∃𝑥 𝑥 = 𝑦 | |
2 | equcomi 1691 | . 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) | |
3 | 1, 2 | eximii 1589 | 1 ⊢ ∃𝑥 𝑦 = 𝑥 |
Colors of variables: wff set class |
Syntax hints: ∃wex 1479 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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