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Mirrors > Home > ILE Home > Th. List > elixp2 | Unicode version |
Description: Membership in an infinite Cartesian product. See df-ixp 6593 for discussion of the notation. (Contributed by NM, 28-Sep-2006.) |
Ref | Expression |
---|---|
elixp2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq1 5211 | . . . . 5 | |
2 | fveq1 5420 | . . . . . . 7 | |
3 | 2 | eleq1d 2208 | . . . . . 6 |
4 | 3 | ralbidv 2437 | . . . . 5 |
5 | 1, 4 | anbi12d 464 | . . . 4 |
6 | dfixp 6594 | . . . 4 | |
7 | 5, 6 | elab2g 2831 | . . 3 |
8 | 7 | pm5.32i 449 | . 2 |
9 | elex 2697 | . . 3 | |
10 | 9 | pm4.71ri 389 | . 2 |
11 | 3anass 966 | . 2 | |
12 | 8, 10, 11 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 962 wceq 1331 wcel 1480 wral 2416 cvv 2686 wfn 5118 cfv 5123 cixp 6592 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fn 5126 df-fv 5131 df-ixp 6593 |
This theorem is referenced by: fvixp 6597 ixpfn 6598 elixp 6599 ixpf 6614 resixp 6627 mptelixpg 6628 |
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