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Mirrors > Home > MPE Home > Th. List > cbvoprab2 | Structured version Visualization version Unicode version |
Description: Change the second bound variable in an operation abstraction. (Contributed by Jeff Madsen, 11-Jun-2010.) (Revised by Mario Carneiro, 11-Dec-2016.) |
Ref | Expression |
---|---|
cbvoprab2.1 | |
cbvoprab2.2 | |
cbvoprab2.3 |
Ref | Expression |
---|---|
cbvoprab2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . . . . . . 7 | |
2 | cbvoprab2.1 | . . . . . . 7 | |
3 | 1, 2 | nfan 1828 | . . . . . 6 |
4 | 3 | nfex 2154 | . . . . 5 |
5 | nfv 1843 | . . . . . . 7 | |
6 | cbvoprab2.2 | . . . . . . 7 | |
7 | 5, 6 | nfan 1828 | . . . . . 6 |
8 | 7 | nfex 2154 | . . . . 5 |
9 | opeq2 4403 | . . . . . . . . 9 | |
10 | 9 | opeq1d 4408 | . . . . . . . 8 |
11 | 10 | eqeq2d 2632 | . . . . . . 7 |
12 | cbvoprab2.3 | . . . . . . 7 | |
13 | 11, 12 | anbi12d 747 | . . . . . 6 |
14 | 13 | exbidv 1850 | . . . . 5 |
15 | 4, 8, 14 | cbvex 2272 | . . . 4 |
16 | 15 | exbii 1774 | . . 3 |
17 | 16 | abbii 2739 | . 2 |
18 | df-oprab 6654 | . 2 | |
19 | df-oprab 6654 | . 2 | |
20 | 17, 18, 19 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wnf 1708 cab 2608 cop 4183 coprab 6651 |
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-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-oprab 6654 |
This theorem is referenced by: cbvmpt22 39277 |
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