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Mirrors > Home > MPE Home > Th. List > copsex2g | Structured version Visualization version Unicode version |
Description: Implicit substitution inference for ordered pairs. (Contributed by NM, 28-May-1995.) |
Ref | Expression |
---|---|
copsex2g.1 |
Ref | Expression |
---|---|
copsex2g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 3215 | . 2 | |
2 | elisset 3215 | . 2 | |
3 | eeanv 2182 | . . 3 | |
4 | nfe1 2027 | . . . . 5 | |
5 | nfv 1843 | . . . . 5 | |
6 | 4, 5 | nfbi 1833 | . . . 4 |
7 | nfe1 2027 | . . . . . . 7 | |
8 | 7 | nfex 2154 | . . . . . 6 |
9 | nfv 1843 | . . . . . 6 | |
10 | 8, 9 | nfbi 1833 | . . . . 5 |
11 | opeq12 4404 | . . . . . . 7 | |
12 | copsexg 4956 | . . . . . . . 8 | |
13 | 12 | eqcoms 2630 | . . . . . . 7 |
14 | 11, 13 | syl 17 | . . . . . 6 |
15 | copsex2g.1 | . . . . . 6 | |
16 | 14, 15 | bitr3d 270 | . . . . 5 |
17 | 10, 16 | exlimi 2086 | . . . 4 |
18 | 6, 17 | exlimi 2086 | . . 3 |
19 | 3, 18 | sylbir 225 | . 2 |
20 | 1, 2, 19 | syl2an 494 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 cop 4183 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 |
This theorem is referenced by: opelopabga 4988 ov6g 6798 ltresr 9961 |
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