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Mirrors > Home > ILE Home > Th. List > ixpm | Unicode version |
Description: If an infinite Cartesian product of a family is inhabited, every is inhabited. (Contributed by Mario Carneiro, 22-Jun-2016.) (Revised by Jim Kingdon, 16-Feb-2023.) |
Ref | Expression |
---|---|
ixpm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ixp 6675 | . . . 4 | |
2 | 1 | abeq2i 2281 | . . 3 |
3 | elex2 2746 | . . . 4 | |
4 | 3 | ralimi 2533 | . . 3 |
5 | 2, 4 | simplbiim 385 | . 2 |
6 | 5 | exlimiv 1591 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1485 wcel 2141 cab 2156 wral 2448 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-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-ral 2453 df-v 2732 df-ixp 6675 |
This theorem is referenced by: ixp0 6707 |
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