Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mpodifsnif | Unicode version |
Description: A mapping with two arguments with the first argument from a difference set with a singleton and a conditional as result. (Contributed by AV, 13-Feb-2019.) |
Ref | Expression |
---|---|
mpodifsnif |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldifsn 3650 | . . . . 5 | |
2 | neneq 2330 | . . . . 5 | |
3 | 1, 2 | simplbiim 384 | . . . 4 |
4 | 3 | adantr 274 | . . 3 |
5 | 4 | iffalsed 3484 | . 2 |
6 | 5 | mpoeq3ia 5836 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wceq 1331 wcel 1480 wne 2308 cdif 3068 cif 3474 csn 3527 cmpo 5776 |
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-in1 603 ax-in2 604 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-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-v 2688 df-dif 3073 df-if 3475 df-sn 3533 df-oprab 5778 df-mpo 5779 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |