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Mirrors > Home > ILE Home > Th. List > axext3 | Unicode version |
Description: A generalization of the Axiom of Extensionality in which and need not be distinct. (Contributed by NM, 15-Sep-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) |
Ref | Expression |
---|---|
axext3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elequ2 2140 | . . . . 5 | |
2 | 1 | bibi1d 232 | . . . 4 |
3 | 2 | albidv 1811 | . . 3 |
4 | equequ1 1699 | . . 3 | |
5 | 3, 4 | imbi12d 233 | . 2 |
6 | ax-ext 2146 | . 2 | |
7 | 5, 6 | chvarv 1924 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 |
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 ax-14 2138 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 |
This theorem is referenced by: axext4 2148 |
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