Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > cbviun | Structured version Visualization version 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 2758 | . . . 4 |
3 | cbviun.2 | . . . . 5 | |
4 | 3 | nfcri 2758 | . . . 4 |
5 | cbviun.3 | . . . . 5 | |
6 | 5 | eleq2d 2687 | . . . 4 |
7 | 2, 4, 6 | cbvrex 3168 | . . 3 |
8 | 7 | abbii 2739 | . 2 |
9 | df-iun 4522 | . 2 | |
10 | df-iun 4522 | . 2 | |
11 | 8, 9, 10 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 cab 2608 wnfc 2751 wrex 2913 ciun 4520 |
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-ral 2917 df-rex 2918 df-iun 4522 |
This theorem is referenced by: cbviunv 4559 disjxiun 4649 disjxiunOLD 4650 funiunfvf 6507 mpt2mptsx 7233 dmmpt2ssx 7235 fmpt2x 7236 ovmptss 7258 iunfi 8254 fsum2dlem 14501 fsumcom2 14505 fsumcom2OLD 14506 fsumiun 14553 fprod2dlem 14710 fprodcom2 14714 fprodcom2OLD 14715 gsumcom2 18374 fiuncmp 21207 ovolfiniun 23269 ovoliunlem3 23272 ovoliun 23273 finiunmbl 23312 volfiniun 23315 iunmbl 23321 limciun 23658 iuneqfzuzlem 39550 fsumiunss 39807 sge0iunmpt 40635 smfliminf 41037 dmmpt2ssx2 42115 |
Copyright terms: Public domain | W3C validator |