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Mirrors > Home > ILE Home > Th. List > ss2ixp | Unicode version |
Description: Subclass theorem for infinite Cartesian product. (Contributed by NM, 29-Sep-2006.) (Revised by Mario Carneiro, 12-Aug-2016.) |
Ref | Expression |
---|---|
ss2ixp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3141 | . . . . 5 | |
2 | 1 | ral2imi 2535 | . . . 4 |
3 | 2 | anim2d 335 | . . 3 |
4 | 3 | ss2abdv 3220 | . 2 |
5 | df-ixp 6675 | . 2 | |
6 | df-ixp 6675 | . 2 | |
7 | 4, 5, 6 | 3sstr4g 3190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2141 cab 2156 wral 2448 wss 3121 wfn 5191 cfv 5196 cixp 6674 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 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-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-in 3127 df-ss 3134 df-ixp 6675 |
This theorem is referenced by: ixpeq2 6688 |
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