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Mirrors > Home > ILE Home > Th. List > dfixp | Unicode version |
Description: Eliminate the expression in df-ixp 6673, under the assumption that and are disjoint. This way, we can say that is bound in even if it appears free in . (Contributed by Mario Carneiro, 12-Aug-2016.) |
Ref | Expression |
---|---|
dfixp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ixp 6673 | . 2 | |
2 | abid2 2291 | . . . . 5 | |
3 | 2 | fneq2i 5291 | . . . 4 |
4 | 3 | anbi1i 455 | . . 3 |
5 | 4 | abbii 2286 | . 2 |
6 | 1, 5 | eqtri 2191 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wcel 2141 cab 2156 wral 2448 wfn 5191 cfv 5196 cixp 6672 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-fn 5199 df-ixp 6673 |
This theorem is referenced by: ixpsnval 6675 elixp2 6676 ixpeq1 6683 cbvixp 6689 ixp0x 6700 |
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