Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > fin | Unicode version |
Description: Mapping into an intersection. (Contributed by NM, 14-Sep-1999.) (Proof shortened by Andrew Salmon, 17-Sep-2011.) |
Ref | Expression |
---|---|
fin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssin 3298 | . . . 4 | |
2 | 1 | anbi2i 452 | . . 3 |
3 | anandi 579 | . . 3 | |
4 | 2, 3 | bitr3i 185 | . 2 |
5 | df-f 5127 | . 2 | |
6 | df-f 5127 | . . 3 | |
7 | df-f 5127 | . . 3 | |
8 | 6, 7 | anbi12i 455 | . 2 |
9 | 4, 5, 8 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 cin 3070 wss 3071 crn 4540 wfn 5118 wf 5119 |
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-v 2688 df-in 3077 df-ss 3084 df-f 5127 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |