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Mirrors > Home > MPE Home > Th. List > inopab | Structured version Visualization version Unicode version |
Description: Intersection of two ordered pair class abstractions. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
inopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relopab 5247 | . . 3 | |
2 | relin1 5236 | . . 3 | |
3 | 1, 2 | ax-mp 5 | . 2 |
4 | relopab 5247 | . 2 | |
5 | sban 2399 | . . . 4 | |
6 | sban 2399 | . . . . 5 | |
7 | 6 | sbbii 1887 | . . . 4 |
8 | opelopabsbALT 4984 | . . . . 5 | |
9 | opelopabsbALT 4984 | . . . . 5 | |
10 | 8, 9 | anbi12i 733 | . . . 4 |
11 | 5, 7, 10 | 3bitr4ri 293 | . . 3 |
12 | elin 3796 | . . 3 | |
13 | opelopabsbALT 4984 | . . 3 | |
14 | 11, 12, 13 | 3bitr4i 292 | . 2 |
15 | 3, 4, 14 | eqrelriiv 5214 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wsb 1880 wcel 1990 cin 3573 cop 4183 copab 4712 wrel 5119 |
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 df-rel 5121 |
This theorem is referenced by: inxp 5254 resopab 5446 fndmin 6324 wemapwe 8594 dfiso2 16432 frgpuplem 18185 ltbwe 19472 opsrtoslem1 19484 pjfval2 20053 lgsquadlem3 25107 dnwech 37618 fgraphopab 37788 |
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