Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > ceqsexg | Structured version Visualization version Unicode version |
Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. (Contributed by NM, 11-Oct-2004.) |
Ref | Expression |
---|---|
ceqsexg.1 | |
ceqsexg.2 |
Ref | Expression |
---|---|
ceqsexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2027 | . . 3 | |
2 | ceqsexg.1 | . . 3 | |
3 | 1, 2 | nfbi 1833 | . 2 |
4 | ceqex 3333 | . . 3 | |
5 | ceqsexg.2 | . . 3 | |
6 | 4, 5 | bibi12d 335 | . 2 |
7 | biid 251 | . 2 | |
8 | 3, 6, 7 | vtoclg1f 3265 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wnf 1708 wcel 1990 |
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-12 2047 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-v 3202 |
This theorem is referenced by: ceqsexgv 3335 |
Copyright terms: Public domain | W3C validator |