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Mirrors > Home > MPE Home > Th. List > vtoclgaf | Structured version Visualization version Unicode version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 17-Feb-2006.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgaf.1 | |
vtoclgaf.2 | |
vtoclgaf.3 | |
vtoclgaf.4 |
Ref | Expression |
---|---|
vtoclgaf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtoclgaf.1 | . . 3 | |
2 | 1 | nfel1 2779 | . . . 4 |
3 | vtoclgaf.2 | . . . 4 | |
4 | 2, 3 | nfim 1825 | . . 3 |
5 | eleq1 2689 | . . . 4 | |
6 | vtoclgaf.3 | . . . 4 | |
7 | 5, 6 | imbi12d 334 | . . 3 |
8 | vtoclgaf.4 | . . 3 | |
9 | 1, 4, 7, 8 | vtoclgf 3264 | . 2 |
10 | 9 | pm2.43i 52 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wnf 1708 wcel 1990 wnfc 2751 |
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-v 3202 |
This theorem is referenced by: vtoclga 3272 ssiun2s 4564 iunopeqop 4981 fvmptss 6292 fvmptf 6301 fmptco 6396 tfis 7054 inar1 9597 sumss 14455 fprodn0 14709 prmind2 15398 lss1d 18963 itg2splitlem 23515 dgrle 23999 cnlnadjlem5 28930 poimirlem25 33434 stoweidlem26 40243 |
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