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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 3708 | . . . . 5 | |
2 | neneq 2362 | . . . . 5 | |
3 | 1, 2 | simplbiim 385 | . . . 4 |
4 | 3 | adantr 274 | . . 3 |
5 | 4 | iffalsed 3535 | . 2 |
6 | 5 | mpoeq3ia 5915 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wceq 1348 wcel 2141 wne 2340 cdif 3118 cif 3525 csn 3581 cmpo 5852 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-v 2732 df-dif 3123 df-if 3526 df-sn 3587 df-oprab 5854 df-mpo 5855 |
This theorem is referenced by: (None) |
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