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Mirrors > Home > MPE Home > Th. List > ralxpf | Structured version Visualization version Unicode version |
Description: Version of ralxp 5263 with bound-variable hypotheses. (Contributed by NM, 18-Aug-2006.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
ralxpf.1 | |
ralxpf.2 | |
ralxpf.3 | |
ralxpf.4 |
Ref | Expression |
---|---|
ralxpf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvralsv 3182 | . 2 | |
2 | cbvralsv 3182 | . . . 4 | |
3 | 2 | ralbii 2980 | . . 3 |
4 | nfv 1843 | . . . 4 | |
5 | nfcv 2764 | . . . . 5 | |
6 | nfs1v 2437 | . . . . 5 | |
7 | 5, 6 | nfral 2945 | . . . 4 |
8 | sbequ12 2111 | . . . . 5 | |
9 | 8 | ralbidv 2986 | . . . 4 |
10 | 4, 7, 9 | cbvral 3167 | . . 3 |
11 | vex 3203 | . . . . . 6 | |
12 | vex 3203 | . . . . . 6 | |
13 | 11, 12 | eqvinop 4955 | . . . . 5 |
14 | ralxpf.1 | . . . . . . . 8 | |
15 | 14 | nfsb 2440 | . . . . . . 7 |
16 | 6 | nfsb 2440 | . . . . . . 7 |
17 | 15, 16 | nfbi 1833 | . . . . . 6 |
18 | ralxpf.2 | . . . . . . . . 9 | |
19 | 18 | nfsb 2440 | . . . . . . . 8 |
20 | nfs1v 2437 | . . . . . . . 8 | |
21 | 19, 20 | nfbi 1833 | . . . . . . 7 |
22 | ralxpf.3 | . . . . . . . . 9 | |
23 | ralxpf.4 | . . . . . . . . 9 | |
24 | 22, 23 | sbhypf 3253 | . . . . . . . 8 |
25 | vex 3203 | . . . . . . . . . 10 | |
26 | vex 3203 | . . . . . . . . . 10 | |
27 | 25, 26 | opth 4945 | . . . . . . . . 9 |
28 | sbequ12 2111 | . . . . . . . . . 10 | |
29 | 8, 28 | sylan9bb 736 | . . . . . . . . 9 |
30 | 27, 29 | sylbi 207 | . . . . . . . 8 |
31 | 24, 30 | sylan9bb 736 | . . . . . . 7 |
32 | 21, 31 | exlimi 2086 | . . . . . 6 |
33 | 17, 32 | exlimi 2086 | . . . . 5 |
34 | 13, 33 | sylbi 207 | . . . 4 |
35 | 34 | ralxp 5263 | . . 3 |
36 | 3, 10, 35 | 3bitr4ri 293 | . 2 |
37 | 1, 36 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wnf 1708 wsb 1880 wral 2912 cop 4183 cxp 5112 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 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-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-iun 4522 df-opab 4713 df-xp 5120 df-rel 5121 |
This theorem is referenced by: rexxpf 5269 |
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