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Mirrors > Home > MPE Home > Th. List > iunopab | Structured version Visualization version Unicode version |
Description: Move indexed union inside an ordered-pair abstraction. (Contributed by Stefan O'Rear, 20-Feb-2015.) |
Ref | Expression |
---|---|
iunopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elopab 4983 | . . . . 5 | |
2 | 1 | rexbii 3041 | . . . 4 |
3 | rexcom4 3225 | . . . . 5 | |
4 | rexcom4 3225 | . . . . . . 7 | |
5 | r19.42v 3092 | . . . . . . . 8 | |
6 | 5 | exbii 1774 | . . . . . . 7 |
7 | 4, 6 | bitri 264 | . . . . . 6 |
8 | 7 | exbii 1774 | . . . . 5 |
9 | 3, 8 | bitri 264 | . . . 4 |
10 | 2, 9 | bitri 264 | . . 3 |
11 | 10 | abbii 2739 | . 2 |
12 | df-iun 4522 | . 2 | |
13 | df-opab 4713 | . 2 | |
14 | 11, 12, 13 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 wex 1704 wcel 1990 cab 2608 wrex 2913 cop 4183 ciun 4520 copab 4712 |
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-ral 2917 df-rex 2918 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-iun 4522 df-opab 4713 |
This theorem is referenced by: marypha2lem2 8342 |
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