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Mirrors > Home > MPE Home > Th. List > rabxp | Structured version Visualization version Unicode version |
Description: Membership in a class builder restricted to a Cartesian product. (Contributed by NM, 20-Feb-2014.) |
Ref | Expression |
---|---|
rabxp.1 |
Ref | Expression |
---|---|
rabxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elxp 5131 | . . . . 5 | |
2 | 1 | anbi1i 731 | . . . 4 |
3 | 19.41vv 1915 | . . . 4 | |
4 | anass 681 | . . . . . 6 | |
5 | rabxp.1 | . . . . . . . . 9 | |
6 | 5 | anbi2d 740 | . . . . . . . 8 |
7 | df-3an 1039 | . . . . . . . 8 | |
8 | 6, 7 | syl6bbr 278 | . . . . . . 7 |
9 | 8 | pm5.32i 669 | . . . . . 6 |
10 | 4, 9 | bitri 264 | . . . . 5 |
11 | 10 | 2exbii 1775 | . . . 4 |
12 | 2, 3, 11 | 3bitr2i 288 | . . 3 |
13 | 12 | abbii 2739 | . 2 |
14 | df-rab 2921 | . 2 | |
15 | df-opab 4713 | . 2 | |
16 | 13, 14, 15 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wex 1704 wcel 1990 cab 2608 crab 2916 cop 4183 copab 4712 cxp 5112 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-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-opab 4713 df-xp 5120 |
This theorem is referenced by: cicer 16466 poimirlem26 33435 dib1dim 36454 diclspsn 36483 fgraphxp 37789 |
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