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Mirrors > Home > ILE Home > Th. List > opabbid | Unicode version |
Description: Equivalent wff's yield equal ordered-pair class abstractions (deduction form). (Contributed by NM, 21-Feb-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
opabbid.1 | |
opabbid.2 | |
opabbid.3 |
Ref | Expression |
---|---|
opabbid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opabbid.1 | . . . 4 | |
2 | opabbid.2 | . . . . 5 | |
3 | opabbid.3 | . . . . . 6 | |
4 | 3 | anbi2d 459 | . . . . 5 |
5 | 2, 4 | exbid 1580 | . . . 4 |
6 | 1, 5 | exbid 1580 | . . 3 |
7 | 6 | abbidv 2235 | . 2 |
8 | df-opab 3960 | . 2 | |
9 | df-opab 3960 | . 2 | |
10 | 7, 8, 9 | 3eqtr4g 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wnf 1421 wex 1453 cab 2103 cop 3500 copab 3958 |
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-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-opab 3960 |
This theorem is referenced by: opabbidv 3964 mpteq12f 3978 fnoprabg 5840 |
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