Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rmob | Unicode version |
Description: Consequence of "at most one", using implicit substitution. (Contributed by NM, 2-Jan-2015.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
rmoi.b | |
rmoi.c |
Ref | Expression |
---|---|
rmob |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2450 | . 2 | |
2 | simprl 521 | . . . 4 | |
3 | eleq1 2227 | . . . 4 | |
4 | 2, 3 | syl5ibcom 154 | . . 3 |
5 | simpl 108 | . . . 4 | |
6 | 5 | a1i 9 | . . 3 |
7 | simplrl 525 | . . . . 5 | |
8 | simpr 109 | . . . . 5 | |
9 | simpll 519 | . . . . 5 | |
10 | simplrr 526 | . . . . 5 | |
11 | eleq1 2227 | . . . . . . 7 | |
12 | rmoi.b | . . . . . . 7 | |
13 | 11, 12 | anbi12d 465 | . . . . . 6 |
14 | eleq1 2227 | . . . . . . 7 | |
15 | rmoi.c | . . . . . . 7 | |
16 | 14, 15 | anbi12d 465 | . . . . . 6 |
17 | 13, 16 | mob 2904 | . . . . 5 |
18 | 7, 8, 9, 7, 10, 17 | syl212anc 1237 | . . . 4 |
19 | 18 | ex 114 | . . 3 |
20 | 4, 6, 19 | pm5.21ndd 695 | . 2 |
21 | 1, 20 | sylanb 282 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wmo 2014 wcel 2135 wrmo 2445 |
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-3an 969 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-nfc 2295 df-rmo 2450 df-v 2724 |
This theorem is referenced by: rmoi 3040 |
Copyright terms: Public domain | W3C validator |