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Mirrors > Home > MPE Home > Th. List > 3optocl | Structured version Visualization version Unicode version |
Description: Implicit substitution of classes for ordered pairs. (Contributed by NM, 12-Mar-1995.) |
Ref | Expression |
---|---|
3optocl.1 | |
3optocl.2 | |
3optocl.3 | |
3optocl.4 | |
3optocl.5 |
Ref | Expression |
---|---|
3optocl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3optocl.1 | . . . 4 | |
2 | 3optocl.4 | . . . . 5 | |
3 | 2 | imbi2d 330 | . . . 4 |
4 | 3optocl.2 | . . . . . . 7 | |
5 | 4 | imbi2d 330 | . . . . . 6 |
6 | 3optocl.3 | . . . . . . 7 | |
7 | 6 | imbi2d 330 | . . . . . 6 |
8 | 3optocl.5 | . . . . . . 7 | |
9 | 8 | 3expia 1267 | . . . . . 6 |
10 | 1, 5, 7, 9 | 2optocl 5196 | . . . . 5 |
11 | 10 | com12 32 | . . . 4 |
12 | 1, 3, 11 | optocl 5195 | . . 3 |
13 | 12 | impcom 446 | . 2 |
14 | 13 | 3impa 1259 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 cop 4183 cxp 5112 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 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 df-opab 4713 df-xp 5120 |
This theorem is referenced by: ecopovtrn 7850 |
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