Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > maxleim | Unicode version |
Description: Value of maximum when we know which number is larger. (Contributed by Jim Kingdon, 21-Dec-2021.) |
Ref | Expression |
---|---|
maxleim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lttri3 7844 | . . . 4 | |
2 | 1 | adantl 275 | . . 3 |
3 | simplr 519 | . . 3 | |
4 | prid2g 3628 | . . . 4 | |
5 | 3, 4 | syl 14 | . . 3 |
6 | simpll 518 | . . . . . . 7 | |
7 | 6 | ad2antrr 479 | . . . . . 6 |
8 | 3 | ad2antrr 479 | . . . . . 6 |
9 | simpllr 523 | . . . . . 6 | |
10 | 7, 8, 9 | lensymd 7884 | . . . . 5 |
11 | breq2 3933 | . . . . . . 7 | |
12 | 11 | notbid 656 | . . . . . 6 |
13 | 12 | adantl 275 | . . . . 5 |
14 | 10, 13 | mpbird 166 | . . . 4 |
15 | 3 | ad2antrr 479 | . . . . . 6 |
16 | 15 | ltnrd 7875 | . . . . 5 |
17 | breq2 3933 | . . . . . . 7 | |
18 | 17 | notbid 656 | . . . . . 6 |
19 | 18 | adantl 275 | . . . . 5 |
20 | 16, 19 | mpbird 166 | . . . 4 |
21 | elpri 3550 | . . . . 5 | |
22 | 21 | adantl 275 | . . . 4 |
23 | 14, 20, 22 | mpjaodan 787 | . . 3 |
24 | 2, 3, 5, 23 | supmaxti 6891 | . 2 |
25 | 24 | ex 114 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wo 697 wceq 1331 wcel 1480 cpr 3528 class class class wbr 3929 csup 6869 cr 7619 clt 7800 cle 7801 |
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-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 ax-cnex 7711 ax-resscn 7712 ax-pre-ltirr 7732 ax-pre-apti 7735 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-nel 2404 df-ral 2421 df-rex 2422 df-reu 2423 df-rmo 2424 df-rab 2425 df-v 2688 df-sbc 2910 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-xp 4545 df-cnv 4547 df-iota 5088 df-riota 5730 df-sup 6871 df-pnf 7802 df-mnf 7803 df-xr 7804 df-ltxr 7805 df-le 7806 |
This theorem is referenced by: maxleb 10988 xrmaxiflemab 11016 |
Copyright terms: Public domain | W3C validator |