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Mirrors > Home > MPE Home > Th. List > cbvex2 | Structured version Visualization version Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 14-Sep-2003.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 16-Jun-2019.) |
Ref | Expression |
---|---|
cbval2.1 | |
cbval2.2 | |
cbval2.3 | |
cbval2.4 | |
cbval2.5 |
Ref | Expression |
---|---|
cbvex2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbval2.1 | . . . . 5 | |
2 | 1 | nfn 1784 | . . . 4 |
3 | cbval2.2 | . . . . 5 | |
4 | 3 | nfn 1784 | . . . 4 |
5 | cbval2.3 | . . . . 5 | |
6 | 5 | nfn 1784 | . . . 4 |
7 | cbval2.4 | . . . . 5 | |
8 | 7 | nfn 1784 | . . . 4 |
9 | cbval2.5 | . . . . 5 | |
10 | 9 | notbid 308 | . . . 4 |
11 | 2, 4, 6, 8, 10 | cbval2 2279 | . . 3 |
12 | 11 | notbii 310 | . 2 |
13 | 2exnaln 1756 | . 2 | |
14 | 2exnaln 1756 | . 2 | |
15 | 12, 13, 14 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 wal 1481 wex 1704 wnf 1708 |
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-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 |
This theorem is referenced by: cbvex2vOLD 2288 cbvopab 4721 cbvoprab12 6729 |
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