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Mirrors > Home > ILE Home > Th. List > dfixp | Unicode version |
Description: Eliminate the expression in df-ixp 6656, 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 6656 | . 2 | |
2 | abid2 2285 | . . . . 5 | |
3 | 2 | fneq2i 5277 | . . . 4 |
4 | 3 | anbi1i 454 | . . 3 |
5 | 4 | abbii 2280 | . 2 |
6 | 1, 5 | eqtri 2185 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1342 wcel 2135 cab 2150 wral 2442 wfn 5177 cfv 5182 cixp 6655 |
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-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-fn 5185 df-ixp 6656 |
This theorem is referenced by: ixpsnval 6658 elixp2 6659 ixpeq1 6666 cbvixp 6672 ixp0x 6683 |
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