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Mirrors > Home > MPE Home > Th. List > 3optocl | 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 316 | . . . 4 |
4 | 3optocl.2 | . . . . . . 7 | |
5 | 4 | imbi2d 316 | . . . . . 6 |
6 | 3optocl.3 | . . . . . . 7 | |
7 | 6 | imbi2d 316 | . . . . . 6 |
8 | 3optocl.5 | . . . . . . 7 | |
9 | 8 | 3expia 1198 | . . . . . 6 |
10 | 1, 5, 7, 9 | 2optocl 5082 | . . . . 5 |
11 | 10 | com12 31 | . . . 4 |
12 | 1, 3, 11 | optocl 5081 | . . 3 |
13 | 12 | impcom 430 | . 2 |
14 | 13 | 3impa 1191 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -> wi 4 <-> wb 184
/\ wa 369 /\ w3a 973 = wceq 1395
e. wcel 1818 <. cop 4035 X. cxp 5002 |
This theorem is referenced by: ecopovtrn 7433 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-9 1822 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 ax-sep 4573 ax-nul 4581 ax-pr 4691 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 975 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-clab 2443 df-cleq 2449 df-clel 2452 df-nfc 2607 df-ne 2654 df-ral 2812 df-rex 2813 df-rab 2816 df-v 3111 df-dif 3478 df-un 3480 df-in 3482 df-ss 3489 df-nul 3785 df-if 3942 df-sn 4030 df-pr 4032 df-op 4036 df-opab 4511 df-xp 5010 |
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