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Mirrors > Home > NFE Home > Th. List > cbvmpt2x | Unicode version |
Description: Rule to change the bound variable in a maps-to function, using implicit substitution. This version of cbvmpt2 5679 allows to be a function of . (Contributed by NM, 29-Dec-2014.) |
Ref | Expression |
---|---|
cbvmpt2x.1 | |
cbvmpt2x.2 | |
cbvmpt2x.3 | |
cbvmpt2x.4 | |
cbvmpt2x.5 | |
cbvmpt2x.6 | |
cbvmpt2x.7 | |
cbvmpt2x.8 |
Ref | Expression |
---|---|
cbvmpt2x |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 | . . . . 5 | |
2 | cbvmpt2x.1 | . . . . . 6 | |
3 | 2 | nfcri 2483 | . . . . 5 |
4 | 1, 3 | nfan 1824 | . . . 4 |
5 | cbvmpt2x.3 | . . . . 5 | |
6 | 5 | nfeq2 2500 | . . . 4 |
7 | 4, 6 | nfan 1824 | . . 3 |
8 | nfv 1619 | . . . . 5 | |
9 | nfcv 2489 | . . . . . 6 | |
10 | 9 | nfcri 2483 | . . . . 5 |
11 | 8, 10 | nfan 1824 | . . . 4 |
12 | cbvmpt2x.4 | . . . . 5 | |
13 | 12 | nfeq2 2500 | . . . 4 |
14 | 11, 13 | nfan 1824 | . . 3 |
15 | nfv 1619 | . . . . 5 | |
16 | cbvmpt2x.2 | . . . . . 6 | |
17 | 16 | nfcri 2483 | . . . . 5 |
18 | 15, 17 | nfan 1824 | . . . 4 |
19 | cbvmpt2x.5 | . . . . 5 | |
20 | 19 | nfeq2 2500 | . . . 4 |
21 | 18, 20 | nfan 1824 | . . 3 |
22 | nfv 1619 | . . . 4 | |
23 | cbvmpt2x.6 | . . . . 5 | |
24 | 23 | nfeq2 2500 | . . . 4 |
25 | 22, 24 | nfan 1824 | . . 3 |
26 | eleq1 2413 | . . . . . 6 | |
27 | 26 | adantr 451 | . . . . 5 |
28 | cbvmpt2x.7 | . . . . . . 7 | |
29 | 28 | eleq2d 2420 | . . . . . 6 |
30 | eleq1 2413 | . . . . . 6 | |
31 | 29, 30 | sylan9bb 680 | . . . . 5 |
32 | 27, 31 | anbi12d 691 | . . . 4 |
33 | cbvmpt2x.8 | . . . . 5 | |
34 | 33 | eqeq2d 2364 | . . . 4 |
35 | 32, 34 | anbi12d 691 | . . 3 |
36 | 7, 14, 21, 25, 35 | cbvoprab12 5569 | . 2 |
37 | df-mpt2 5654 | . 2 | |
38 | df-mpt2 5654 | . 2 | |
39 | 36, 37, 38 | 3eqtr4i 2383 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wceq 1642 wcel 1710 wnfc 2476 coprab 5527 cmpt2 5653 |
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 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-3an 936 df-nan 1288 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-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-symdif 3216 df-ss 3259 df-nul 3551 df-if 3663 df-pw 3724 df-sn 3741 df-pr 3742 df-uni 3892 df-int 3927 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-addc 4378 df-nnc 4379 df-phi 4565 df-op 4566 df-opab 4623 df-oprab 5528 df-mpt2 5654 |
This theorem is referenced by: cbvmpt2 5679 |
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