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Mirrors > Home > ILE Home > Th. List > iotajust | Unicode version |
Description: Soundness justification theorem for df-iota 5088. (Contributed by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
iotajust |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sneq 3538 | . . . . 5 | |
2 | 1 | eqeq2d 2151 | . . . 4 |
3 | 2 | cbvabv 2264 | . . 3 |
4 | sneq 3538 | . . . . 5 | |
5 | 4 | eqeq2d 2151 | . . . 4 |
6 | 5 | cbvabv 2264 | . . 3 |
7 | 3, 6 | eqtri 2160 | . 2 |
8 | 7 | unieqi 3746 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 cab 2125 csn 3527 cuni 3736 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-sn 3533 df-uni 3737 |
This theorem is referenced by: (None) |
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