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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 6642 | . 2 | |
2 | ralsnsg 3596 | . . . . 5 | |
3 | sbcel12g 3046 | . . . . 5 | |
4 | csbfvg 5505 | . . . . . 6 | |
5 | 4 | eleq1d 2226 | . . . . 5 |
6 | 2, 3, 5 | 3bitrd 213 | . . . 4 |
7 | 6 | anbi2d 460 | . . 3 |
8 | 7 | abbidv 2275 | . 2 |
9 | 1, 8 | syl5eq 2202 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 cab 2143 wral 2435 wsbc 2937 csb 3031 csn 3560 wfn 5164 cfv 5169 cixp 6640 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-iota 5134 df-fn 5172 df-fv 5177 df-ixp 6641 |
This theorem is referenced by: (None) |
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