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Mirrors > Home > NFE Home > Th. List > cbvopab | Unicode version |
Description: Rule used to change bound variables in an ordered-pair class abstraction, using implicit substitution. (Contributed by NM, 14-Sep-2003.) |
Ref | Expression |
---|---|
cbvopab.1 | |
cbvopab.2 | |
cbvopab.3 | |
cbvopab.4 | |
cbvopab.5 |
Ref | Expression |
---|---|
cbvopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 | . . . . 5 | |
2 | cbvopab.1 | . . . . 5 | |
3 | 1, 2 | nfan 1824 | . . . 4 |
4 | nfv 1619 | . . . . 5 | |
5 | cbvopab.2 | . . . . 5 | |
6 | 4, 5 | nfan 1824 | . . . 4 |
7 | nfv 1619 | . . . . 5 | |
8 | cbvopab.3 | . . . . 5 | |
9 | 7, 8 | nfan 1824 | . . . 4 |
10 | nfv 1619 | . . . . 5 | |
11 | cbvopab.4 | . . . . 5 | |
12 | 10, 11 | nfan 1824 | . . . 4 |
13 | opeq12 4580 | . . . . . 6 | |
14 | 13 | eqeq2d 2364 | . . . . 5 |
15 | cbvopab.5 | . . . . 5 | |
16 | 14, 15 | anbi12d 691 | . . . 4 |
17 | 3, 6, 9, 12, 16 | cbvex2 2005 | . . 3 |
18 | 17 | abbii 2465 | . 2 |
19 | df-opab 4623 | . 2 | |
20 | df-opab 4623 | . 2 | |
21 | 18, 19, 20 | 3eqtr4i 2383 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wex 1541 wnf 1544 wceq 1642 cab 2339 cop 4561 copab 4622 |
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 |
This theorem is referenced by: cbvopabv 4631 |
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