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Mirrors > Home > MPE Home > Th. List > ss2ixp | Structured version Visualization version Unicode version |
Description: Subclass theorem for infinite Cartesian product. (Contributed by NM, 29-Sep-2006.) (Revised by Mario Carneiro, 12-Aug-2016.) |
Ref | Expression |
---|---|
ss2ixp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3597 | . . . . 5 | |
2 | 1 | ral2imi 2947 | . . . 4 |
3 | 2 | anim2d 589 | . . 3 |
4 | 3 | ss2abdv 3675 | . 2 |
5 | df-ixp 7909 | . 2 | |
6 | df-ixp 7909 | . 2 | |
7 | 4, 5, 6 | 3sstr4g 3646 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wcel 1990 cab 2608 wral 2912 wss 3574 wfn 5883 cfv 5888 cixp 7908 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-in 3581 df-ss 3588 df-ixp 7909 |
This theorem is referenced by: ixpeq2 7922 boxcutc 7951 pwcfsdom 9405 prdsval 16115 prdshom 16127 sscpwex 16475 wunfunc 16559 wunnat 16616 dprdss 18428 psrbaglefi 19372 ptuni2 21379 ptcld 21416 ptclsg 21418 prdstopn 21431 xkopt 21458 tmdgsum2 21900 ressprdsds 22176 prdsbl 22296 ptrecube 33409 prdstotbnd 33593 ixpssixp 39269 ioorrnopnxrlem 40526 ovnlecvr2 40824 |
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