New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > cbval | Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) |
Ref | Expression |
---|---|
cbval.1 | |
cbval.2 | |
cbval.3 |
Ref | Expression |
---|---|
cbval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbval.1 | . . 3 | |
2 | cbval.2 | . . 3 | |
3 | cbval.3 | . . . 4 | |
4 | 3 | biimpd 198 | . . 3 |
5 | 1, 2, 4 | cbv3 1982 | . 2 |
6 | 3 | biimprd 214 | . . . 4 |
7 | 6 | equcoms 1681 | . . 3 |
8 | 2, 1, 7 | cbv3 1982 | . 2 |
9 | 5, 8 | impbii 180 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wal 1540 wnf 1544 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: cbvex 1985 cbvalv 2002 cbval2 2004 sb8eu 2222 abbi 2463 cleqf 2513 cbvralf 2829 ralab2 3001 cbvralcsf 3198 dfss2f 3264 elintab 3937 cbviota 4344 sb8iota 4346 dffun6f 5123 |
Copyright terms: Public domain | W3C validator |