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Mirrors > Home > ILE Home > Th. List > elixp2 | Unicode version |
Description: Membership in an infinite Cartesian product. See df-ixp 6656 for discussion of the notation. (Contributed by NM, 28-Sep-2006.) |
Ref | Expression |
---|---|
elixp2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq1 5270 | . . . . 5 | |
2 | fveq1 5479 | . . . . . . 7 | |
3 | 2 | eleq1d 2233 | . . . . . 6 |
4 | 3 | ralbidv 2464 | . . . . 5 |
5 | 1, 4 | anbi12d 465 | . . . 4 |
6 | dfixp 6657 | . . . 4 | |
7 | 5, 6 | elab2g 2868 | . . 3 |
8 | 7 | pm5.32i 450 | . 2 |
9 | elex 2732 | . . 3 | |
10 | 9 | pm4.71ri 390 | . 2 |
11 | 3anass 971 | . 2 | |
12 | 8, 10, 11 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 967 wceq 1342 wcel 2135 wral 2442 cvv 2721 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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 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-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fn 5185 df-fv 5190 df-ixp 6656 |
This theorem is referenced by: fvixp 6660 ixpfn 6661 elixp 6662 ixpf 6677 resixp 6690 mptelixpg 6691 |
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