Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > csbunigOLD | Structured version Visualization version Unicode version |
Description: Distribute proper substitution through the union of a class. (Contributed by Alan Sare, 10-Nov-2012.) Obsolete as of 22-Aug-2018. Use csbuni 4466 instead. (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
csbunigOLD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbabgOLD 39050 | . . 3 | |
2 | sbcexgOLD 38753 | . . . . 5 | |
3 | sbcangOLD 38739 | . . . . . . 7 | |
4 | sbcg 3503 | . . . . . . . 8 | |
5 | sbcel2gOLD 38755 | . . . . . . . 8 | |
6 | 4, 5 | anbi12d 747 | . . . . . . 7 |
7 | 3, 6 | bitrd 268 | . . . . . 6 |
8 | 7 | exbidv 1850 | . . . . 5 |
9 | 2, 8 | bitrd 268 | . . . 4 |
10 | 9 | abbidv 2741 | . . 3 |
11 | 1, 10 | eqtrd 2656 | . 2 |
12 | df-uni 4437 | . . 3 | |
13 | 12 | csbeq2i 3993 | . 2 |
14 | df-uni 4437 | . 2 | |
15 | 11, 13, 14 | 3eqtr4g 2681 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wex 1704 wcel 1990 cab 2608 wsbc 3435 csb 3533 cuni 4436 |
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-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-uni 4437 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |