Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > reusv1 | Unicode version |
Description: Two ways to express single-valuedness of a class expression . (Contributed by NM, 16-Dec-2012.) (Proof shortened by Mario Carneiro, 18-Nov-2016.) |
Ref | Expression |
---|---|
reusv1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 2469 | . . . 4 | |
2 | 1 | nfmo 2020 | . . 3 |
3 | rsp 2483 | . . . . . . . 8 | |
4 | 3 | impd 252 | . . . . . . 7 |
5 | 4 | com12 30 | . . . . . 6 |
6 | 5 | alrimiv 1847 | . . . . 5 |
7 | moeq 2863 | . . . . 5 | |
8 | moim 2064 | . . . . 5 | |
9 | 6, 7, 8 | mpisyl 1423 | . . . 4 |
10 | 9 | ex 114 | . . 3 |
11 | 2, 10 | rexlimi 2545 | . 2 |
12 | mormo 2645 | . 2 | |
13 | reu5 2646 | . . 3 | |
14 | 13 | rbaib 907 | . 2 |
15 | 11, 12, 14 | 3syl 17 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1330 wceq 1332 wcel 1481 wmo 2001 wral 2417 wrex 2418 wreu 2419 wrmo 2420 |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-ral 2422 df-rex 2423 df-reu 2424 df-rmo 2425 df-v 2691 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |