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Mirrors > Home > NFE Home > Th. List > cbvrexcsf | Unicode version |
Description: A more general version of cbvrexf 2830 that has no distinct variable restrictions. Changes bound variables using implicit substitution. (Contributed by Andrew Salmon, 13-Jul-2011.) (Proof shortened by Mario Carneiro, 7-Dec-2014.) |
Ref | Expression |
---|---|
cbvralcsf.1 | |
cbvralcsf.2 | |
cbvralcsf.3 | |
cbvralcsf.4 | |
cbvralcsf.5 | |
cbvralcsf.6 |
Ref | Expression |
---|---|
cbvrexcsf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvralcsf.1 | . . . 4 | |
2 | cbvralcsf.2 | . . . 4 | |
3 | cbvralcsf.3 | . . . . 5 | |
4 | 3 | nfn 1793 | . . . 4 |
5 | cbvralcsf.4 | . . . . 5 | |
6 | 5 | nfn 1793 | . . . 4 |
7 | cbvralcsf.5 | . . . 4 | |
8 | cbvralcsf.6 | . . . . 5 | |
9 | 8 | notbid 285 | . . . 4 |
10 | 1, 2, 4, 6, 7, 9 | cbvralcsf 3198 | . . 3 |
11 | 10 | notbii 287 | . 2 |
12 | dfrex2 2627 | . 2 | |
13 | dfrex2 2627 | . 2 | |
14 | 11, 12, 13 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wnf 1544 wceq 1642 wnfc 2476 wral 2614 wrex 2615 |
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 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-sbc 3047 df-csb 3137 |
This theorem is referenced by: cbvrexv2 3203 |
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