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Mirrors > Home > MPE Home > Th. List > Mathboxes > csbmpt22g | Structured version Visualization version Unicode version |
Description: Move class substitution in and out of maps-to notation for operations. (Contributed by ML, 25-Oct-2020.) |
Ref | Expression |
---|---|
csbmpt22g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csboprabg 33176 | . . 3 | |
2 | sbcan 3478 | . . . . 5 | |
3 | sbcan 3478 | . . . . . . 7 | |
4 | sbcel12 3983 | . . . . . . . . 9 | |
5 | csbconstg 3546 | . . . . . . . . . 10 | |
6 | 5 | eleq1d 2686 | . . . . . . . . 9 |
7 | 4, 6 | syl5bb 272 | . . . . . . . 8 |
8 | sbcel12 3983 | . . . . . . . . 9 | |
9 | csbconstg 3546 | . . . . . . . . . 10 | |
10 | 9 | eleq1d 2686 | . . . . . . . . 9 |
11 | 8, 10 | syl5bb 272 | . . . . . . . 8 |
12 | 7, 11 | anbi12d 747 | . . . . . . 7 |
13 | 3, 12 | syl5bb 272 | . . . . . 6 |
14 | sbceq2g 3990 | . . . . . 6 | |
15 | 13, 14 | anbi12d 747 | . . . . 5 |
16 | 2, 15 | syl5bb 272 | . . . 4 |
17 | 16 | oprabbidv 6709 | . . 3 |
18 | 1, 17 | eqtrd 2656 | . 2 |
19 | df-mpt2 6655 | . . 3 | |
20 | 19 | csbeq2i 3993 | . 2 |
21 | df-mpt2 6655 | . 2 | |
22 | 18, 20, 21 | 3eqtr4g 2681 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wsbc 3435 csb 3533 coprab 6651 cmpt2 6652 |
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-tru 1486 df-fal 1489 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-nul 3916 df-oprab 6654 df-mpt2 6655 |
This theorem is referenced by: csbfinxpg 33225 |
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