Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > csbab | Structured version Visualization version Unicode version |
Description: Move substitution into a class abstraction. (Contributed by NM, 13-Dec-2005.) (Revised by NM, 19-Aug-2018.) |
Ref | Expression |
---|---|
csbab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clab 2609 | . . . 4 | |
2 | sbsbc 3439 | . . . 4 | |
3 | 1, 2 | bitri 264 | . . 3 |
4 | sbccom 3509 | . . . 4 | |
5 | df-clab 2609 | . . . . . 6 | |
6 | sbsbc 3439 | . . . . . 6 | |
7 | 5, 6 | bitri 264 | . . . . 5 |
8 | 7 | sbcbii 3491 | . . . 4 |
9 | 4, 8 | bitr4i 267 | . . 3 |
10 | sbcel2 3989 | . . 3 | |
11 | 3, 9, 10 | 3bitrri 287 | . 2 |
12 | 11 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wsb 1880 wcel 1990 cab 2608 wsbc 3435 csb 3533 |
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 |
This theorem is referenced by: csbsng 4243 csbuni 4466 csbxp 5200 csbdm 5318 csbwrdg 13334 abfmpeld 29454 abfmpel 29455 csbwrecsg 33173 csboprabg 33176 csbfinxpg 33225 csbfv12gALTOLD 39052 csbfv12gALTVD 39135 |
Copyright terms: Public domain | W3C validator |