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Mirrors > Home > MPE Home > Th. List > pltval3 | Structured version Visualization version Unicode version |
Description: Alternate expression for less-than relation. (dfpss3 3693 analog.) (Contributed by NM, 4-Nov-2011.) |
Ref | Expression |
---|---|
pleval2.b | |
pleval2.l | |
pleval2.s |
Ref | Expression |
---|---|
pltval3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pleval2.l | . . 3 | |
2 | pleval2.s | . . 3 | |
3 | 1, 2 | pltval 16960 | . 2 |
4 | pleval2.b | . . . . . . . . 9 | |
5 | 4, 1 | posref 16951 | . . . . . . . 8 |
6 | 5 | 3adant3 1081 | . . . . . . 7 |
7 | breq1 4656 | . . . . . . 7 | |
8 | 6, 7 | syl5ibcom 235 | . . . . . 6 |
9 | 8 | adantr 481 | . . . . 5 |
10 | 4, 1 | posasymb 16952 | . . . . . . 7 |
11 | 10 | biimpd 219 | . . . . . 6 |
12 | 11 | expdimp 453 | . . . . 5 |
13 | 9, 12 | impbid 202 | . . . 4 |
14 | 13 | necon3abid 2830 | . . 3 |
15 | 14 | pm5.32da 673 | . 2 |
16 | 3, 15 | bitrd 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 wne 2794 class class class wbr 4653 cfv 5888 cbs 15857 cple 15948 cpo 16940 cplt 16941 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-preset 16928 df-poset 16946 df-plt 16958 |
This theorem is referenced by: tltnle 29662 opltcon3b 34491 |
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