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Mirrors > Home > NFE Home > Th. List > cbviun | Unicode version |
Description: Rule used to change the bound variables in an indexed union, with the substitution specified implicitly by the hypothesis. (Contributed by NM, 26-Mar-2006.) (Revised by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
cbviun.1 | |
cbviun.2 | |
cbviun.3 |
Ref | Expression |
---|---|
cbviun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbviun.1 | . . . . 5 | |
2 | 1 | nfcri 2483 | . . . 4 |
3 | cbviun.2 | . . . . 5 | |
4 | 3 | nfcri 2483 | . . . 4 |
5 | cbviun.3 | . . . . 5 | |
6 | 5 | eleq2d 2420 | . . . 4 |
7 | 2, 4, 6 | cbvrex 2832 | . . 3 |
8 | 7 | abbii 2465 | . 2 |
9 | df-iun 3971 | . 2 | |
10 | df-iun 3971 | . 2 | |
11 | 8, 9, 10 | 3eqtr4i 2383 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 wcel 1710 cab 2339 wnfc 2476 wrex 2615 ciun 3969 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-rex 2620 df-iun 3971 |
This theorem is referenced by: cbviunv 4005 funiunfvf 5468 fmpt2x 5730 |
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