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Mirrors > Home > NFE Home > Th. List > ralxpf | Unicode version |
Description: Version of ralxp 4825 with bound-variable hypotheses. (Contributed by NM, 18-Aug-2006.) (Revised by set.mm contributors, 20-Dec-2008.) |
Ref | Expression |
---|---|
ralxpf.1 | |
ralxpf.2 | |
ralxpf.3 | |
ralxpf.4 |
Ref | Expression |
---|---|
ralxpf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvralsv 2846 | . 2 | |
2 | cbvralsv 2846 | . . . 4 | |
3 | 2 | ralbii 2638 | . . 3 |
4 | nfv 1619 | . . . 4 | |
5 | nfcv 2489 | . . . . 5 | |
6 | nfv 1619 | . . . . . 6 | |
7 | 6 | nfs1 2044 | . . . . 5 |
8 | 5, 7 | nfral 2667 | . . . 4 |
9 | sbequ12 1919 | . . . . 5 | |
10 | 9 | ralbidv 2634 | . . . 4 |
11 | 4, 8, 10 | cbvral 2831 | . . 3 |
12 | vex 2862 | . . . . . 6 | |
13 | vex 2862 | . . . . . 6 | |
14 | 12, 13 | eqvinop 4606 | . . . . 5 |
15 | ralxpf.1 | . . . . . . . 8 | |
16 | 15 | nfsb 2109 | . . . . . . 7 |
17 | 7 | nfsb 2109 | . . . . . . 7 |
18 | 16, 17 | nfbi 1834 | . . . . . 6 |
19 | ralxpf.2 | . . . . . . . . 9 | |
20 | 19 | nfsb 2109 | . . . . . . . 8 |
21 | nfv 1619 | . . . . . . . . 9 | |
22 | 21 | nfs1 2044 | . . . . . . . 8 |
23 | 20, 22 | nfbi 1834 | . . . . . . 7 |
24 | ralxpf.3 | . . . . . . . . 9 | |
25 | ralxpf.4 | . . . . . . . . 9 | |
26 | 24, 25 | sbhypf 2904 | . . . . . . . 8 |
27 | opth 4602 | . . . . . . . . 9 | |
28 | sbequ12 1919 | . . . . . . . . . 10 | |
29 | 9, 28 | sylan9bb 680 | . . . . . . . . 9 |
30 | 27, 29 | sylbi 187 | . . . . . . . 8 |
31 | 26, 30 | sylan9bb 680 | . . . . . . 7 |
32 | 23, 31 | exlimi 1803 | . . . . . 6 |
33 | 18, 32 | exlimi 1803 | . . . . 5 |
34 | 14, 33 | sylbi 187 | . . . 4 |
35 | 34 | ralxp 4825 | . . 3 |
36 | 3, 11, 35 | 3bitr4ri 269 | . 2 |
37 | 1, 36 | bitri 240 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wex 1541 wnf 1544 wceq 1642 wsb 1648 wral 2614 cop 4561 cxp 4770 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-13 1712 ax-14 1714 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-xp 4079 ax-cnv 4080 ax-1c 4081 ax-sset 4082 ax-si 4083 ax-ins2 4084 ax-ins3 4085 ax-typlower 4086 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3or 935 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-reu 2621 df-rmo 2622 df-rab 2623 df-v 2861 df-sbc 3047 df-csb 3137 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-symdif 3216 df-ss 3259 df-pss 3261 df-nul 3551 df-if 3663 df-pw 3724 df-sn 3741 df-pr 3742 df-uni 3892 df-int 3927 df-iun 3971 df-opk 4058 df-1c 4136 df-pw1 4137 df-uni1 4138 df-xpk 4185 df-cnvk 4186 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-cok 4190 df-p6 4191 df-sik 4192 df-ssetk 4193 df-imagek 4194 df-idk 4195 df-iota 4339 df-0c 4377 df-addc 4378 df-nnc 4379 df-fin 4380 df-lefin 4440 df-ltfin 4441 df-ncfin 4442 df-tfin 4443 df-evenfin 4444 df-oddfin 4445 df-sfin 4446 df-spfin 4447 df-phi 4565 df-op 4566 df-proj1 4567 df-proj2 4568 df-opab 4623 df-xp 4784 |
This theorem is referenced by: rexxpf 4828 |
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