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Mirrors > Home > ILE Home > Th. List > 2optocl | Unicode version |
Description: Implicit substitution of classes for ordered pairs. (Contributed by NM, 12-Mar-1995.) |
Ref | Expression |
---|---|
2optocl.1 | |
2optocl.2 | |
2optocl.3 | |
2optocl.4 |
Ref | Expression |
---|---|
2optocl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2optocl.1 | . . 3 | |
2 | 2optocl.3 | . . . 4 | |
3 | 2 | imbi2d 229 | . . 3 |
4 | 2optocl.2 | . . . . . 6 | |
5 | 4 | imbi2d 229 | . . . . 5 |
6 | 2optocl.4 | . . . . . 6 | |
7 | 6 | ex 114 | . . . . 5 |
8 | 1, 5, 7 | optocl 4615 | . . . 4 |
9 | 8 | com12 30 | . . 3 |
10 | 1, 3, 9 | optocl 4615 | . 2 |
11 | 10 | impcom 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 cop 3530 cxp 4537 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-opab 3990 df-xp 4545 |
This theorem is referenced by: 3optocl 4617 ecopovsym 6525 ecopovsymg 6528 th3qlem2 6532 axaddcom 7678 |
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