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Mirrors > Home > MPE Home > Th. List > cbvralcsf | Structured version Visualization version Unicode version |
Description: A more general version of cbvralf 3165 that doesn't require and to be distinct from or . Changes bound variables using implicit substitution. (Contributed by Andrew Salmon, 13-Jul-2011.) |
Ref | Expression |
---|---|
cbvralcsf.1 | |
cbvralcsf.2 | |
cbvralcsf.3 | |
cbvralcsf.4 | |
cbvralcsf.5 | |
cbvralcsf.6 |
Ref | Expression |
---|---|
cbvralcsf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . . . 4 | |
2 | nfcsb1v 3549 | . . . . . 6 | |
3 | 2 | nfcri 2758 | . . . . 5 |
4 | nfsbc1v 3455 | . . . . 5 | |
5 | 3, 4 | nfim 1825 | . . . 4 |
6 | id 22 | . . . . . 6 | |
7 | csbeq1a 3542 | . . . . . 6 | |
8 | 6, 7 | eleq12d 2695 | . . . . 5 |
9 | sbceq1a 3446 | . . . . 5 | |
10 | 8, 9 | imbi12d 334 | . . . 4 |
11 | 1, 5, 10 | cbval 2271 | . . 3 |
12 | nfcv 2764 | . . . . . . 7 | |
13 | cbvralcsf.1 | . . . . . . 7 | |
14 | 12, 13 | nfcsb 3551 | . . . . . 6 |
15 | 14 | nfcri 2758 | . . . . 5 |
16 | cbvralcsf.3 | . . . . . 6 | |
17 | 12, 16 | nfsbc 3457 | . . . . 5 |
18 | 15, 17 | nfim 1825 | . . . 4 |
19 | nfv 1843 | . . . 4 | |
20 | id 22 | . . . . . 6 | |
21 | csbeq1 3536 | . . . . . . 7 | |
22 | df-csb 3534 | . . . . . . . 8 | |
23 | cbvralcsf.2 | . . . . . . . . . . . 12 | |
24 | 23 | nfcri 2758 | . . . . . . . . . . 11 |
25 | cbvralcsf.5 | . . . . . . . . . . . 12 | |
26 | 25 | eleq2d 2687 | . . . . . . . . . . 11 |
27 | 24, 26 | sbie 2408 | . . . . . . . . . 10 |
28 | sbsbc 3439 | . . . . . . . . . 10 | |
29 | 27, 28 | bitr3i 266 | . . . . . . . . 9 |
30 | 29 | abbi2i 2738 | . . . . . . . 8 |
31 | 22, 30 | eqtr4i 2647 | . . . . . . 7 |
32 | 21, 31 | syl6eq 2672 | . . . . . 6 |
33 | 20, 32 | eleq12d 2695 | . . . . 5 |
34 | dfsbcq 3437 | . . . . . 6 | |
35 | sbsbc 3439 | . . . . . . 7 | |
36 | cbvralcsf.4 | . . . . . . . 8 | |
37 | cbvralcsf.6 | . . . . . . . 8 | |
38 | 36, 37 | sbie 2408 | . . . . . . 7 |
39 | 35, 38 | bitr3i 266 | . . . . . 6 |
40 | 34, 39 | syl6bb 276 | . . . . 5 |
41 | 33, 40 | imbi12d 334 | . . . 4 |
42 | 18, 19, 41 | cbval 2271 | . . 3 |
43 | 11, 42 | bitri 264 | . 2 |
44 | df-ral 2917 | . 2 | |
45 | df-ral 2917 | . 2 | |
46 | 43, 44, 45 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wceq 1483 wnf 1708 wsb 1880 wcel 1990 cab 2608 wnfc 2751 wral 2912 wsbc 3435 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-ral 2917 df-sbc 3436 df-csb 3534 |
This theorem is referenced by: cbvrexcsf 3566 cbvralv2 3569 |
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