Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > cbvcsbv | Structured version Visualization version Unicode version |
Description: Change the bound variable of a proper substitution into a class using implicit substitution. (Contributed by NM, 30-Sep-2008.) (Revised by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
cbvcsbv.1 |
Ref | Expression |
---|---|
cbvcsbv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2764 | . 2 | |
2 | nfcv 2764 | . 2 | |
3 | cbvcsbv.1 | . 2 | |
4 | 1, 2, 3 | cbvcsb 3538 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 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-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-sbc 3436 df-csb 3534 |
This theorem is referenced by: pmatcollpw3lem 20588 poimirlem27 33436 cdleme40v 35757 |
Copyright terms: Public domain | W3C validator |