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Mirrors > Home > ILE Home > Th. List > dfif6 | Unicode version |
Description: An alternate definition of the conditional operator df-if 3470 as a simple class abstraction. (Contributed by Mario Carneiro, 8-Sep-2013.) |
Ref | Expression |
---|---|
dfif6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unab 3338 | . 2 | |
2 | df-rab 2423 | . . 3 | |
3 | df-rab 2423 | . . 3 | |
4 | 2, 3 | uneq12i 3223 | . 2 |
5 | df-if 3470 | . 2 | |
6 | 1, 4, 5 | 3eqtr4ri 2169 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wo 697 wceq 1331 wcel 1480 cab 2123 crab 2418 cun 3064 cif 3469 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rab 2423 df-v 2683 df-un 3070 df-if 3470 |
This theorem is referenced by: ifeq1 3472 ifeq2 3473 dfif3 3482 |
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