Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mosubt | Unicode version |
Description: "At most one" remains true after substitution. (Contributed by Jim Kingdon, 18-Jan-2019.) |
Ref | Expression |
---|---|
mosubt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eueq 2893 | . . . . . 6 | |
2 | isset 2728 | . . . . . 6 | |
3 | 1, 2 | bitr3i 185 | . . . . 5 |
4 | nfv 1515 | . . . . . 6 | |
5 | 4 | euexex 2098 | . . . . 5 |
6 | 3, 5 | sylanbr 283 | . . . 4 |
7 | 6 | expcom 115 | . . 3 |
8 | moanimv 2088 | . . 3 | |
9 | 7, 8 | sylibr 133 | . 2 |
10 | simpl 108 | . . . . 5 | |
11 | 10 | eximi 1587 | . . . 4 |
12 | 11 | ancri 322 | . . 3 |
13 | 12 | moimi 2078 | . 2 |
14 | 9, 13 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1340 wceq 1342 wex 1479 weu 2013 wmo 2014 wcel 2135 cvv 2722 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-v 2724 |
This theorem is referenced by: mosub 2900 |
Copyright terms: Public domain | W3C validator |