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Mirrors > Home > MPE Home > Th. List > ixpin | Structured version Visualization version Unicode version |
Description: The intersection of two infinite Cartesian products. (Contributed by Mario Carneiro, 3-Feb-2015.) |
Ref | Expression |
---|---|
ixpin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anandi 871 | . . . 4 | |
2 | elin 3796 | . . . . . . 7 | |
3 | 2 | ralbii 2980 | . . . . . 6 |
4 | r19.26 3064 | . . . . . 6 | |
5 | 3, 4 | bitri 264 | . . . . 5 |
6 | 5 | anbi2i 730 | . . . 4 |
7 | vex 3203 | . . . . . 6 | |
8 | 7 | elixp 7915 | . . . . 5 |
9 | 7 | elixp 7915 | . . . . 5 |
10 | 8, 9 | anbi12i 733 | . . . 4 |
11 | 1, 6, 10 | 3bitr4i 292 | . . 3 |
12 | 7 | elixp 7915 | . . 3 |
13 | elin 3796 | . . 3 | |
14 | 11, 12, 13 | 3bitr4i 292 | . 2 |
15 | 14 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wcel 1990 wral 2912 cin 3573 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-3an 1039 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-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 df-ixp 7909 |
This theorem is referenced by: ptbasin 21380 ptclsg 21418 ptrest 33408 |
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