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Mirrors > Home > ILE Home > Th. List > ixpsnval | Unicode version |
Description: The value of an infinite Cartesian product with a singleton. (Contributed by AV, 3-Dec-2018.) |
Ref | Expression |
---|---|
ixpsnval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfixp 6678 | . 2 | |
2 | ralsnsg 3620 | . . . . 5 | |
3 | sbcel12g 3064 | . . . . 5 | |
4 | csbfvg 5534 | . . . . . 6 | |
5 | 4 | eleq1d 2239 | . . . . 5 |
6 | 2, 3, 5 | 3bitrd 213 | . . . 4 |
7 | 6 | anbi2d 461 | . . 3 |
8 | 7 | abbidv 2288 | . 2 |
9 | 1, 8 | eqtrid 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 cab 2156 wral 2448 wsbc 2955 csb 3049 csn 3583 wfn 5193 cfv 5198 cixp 6676 |
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-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-csb 3050 df-un 3125 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-iota 5160 df-fn 5201 df-fv 5206 df-ixp 6677 |
This theorem is referenced by: (None) |
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