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Mirrors > Home > ILE 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 229 | . . . 4 |
4 | 3optocl.2 | . . . . . . 7 | |
5 | 4 | imbi2d 229 | . . . . . 6 |
6 | 3optocl.3 | . . . . . . 7 | |
7 | 6 | imbi2d 229 | . . . . . 6 |
8 | 3optocl.5 | . . . . . . 7 | |
9 | 8 | 3expia 1200 | . . . . . 6 |
10 | 1, 5, 7, 9 | 2optocl 4688 | . . . . 5 |
11 | 10 | com12 30 | . . . 4 |
12 | 1, 3, 11 | optocl 4687 | . . 3 |
13 | 12 | impcom 124 | . 2 |
14 | 13 | 3impa 1189 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 973 wceq 1348 wcel 2141 cop 3586 cxp 4609 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-opab 4051 df-xp 4617 |
This theorem is referenced by: ecopovtrn 6610 ecopovtrng 6613 |
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