Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 6593 | . . . 4 | |
2 | 1 | abeq2i 2250 | . . 3 |
3 | elex2 2702 | . . . 4 | |
4 | 3 | ralimi 2495 | . . 3 |
5 | 2, 4 | simplbiim 384 | . 2 |
6 | 5 | exlimiv 1577 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1468 wcel 1480 cab 2125 wral 2416 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-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-ral 2421 df-v 2688 df-ixp 6593 |
This theorem is referenced by: ixp0 6625 |
Copyright terms: Public domain | W3C validator |