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Mirrors > Home > MPE Home > Th. List > eltp | Structured version Visualization version Unicode version |
Description: A member of an unordered triple of classes is one of them. Special case of Exercise 1 of [TakeutiZaring] p. 17. (Contributed by NM, 8-Apr-1994.) (Revised by Mario Carneiro, 11-Feb-2015.) |
Ref | Expression |
---|---|
eltp.1 |
Ref | Expression |
---|---|
eltp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eltp.1 | . 2 | |
2 | eltpg 4227 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 w3o 1036 wceq 1483 wcel 1990 cvv 3200 ctp 4181 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-sn 4178 df-pr 4180 df-tp 4182 |
This theorem is referenced by: dftp2 4231 tpid1 4303 tpid2 4304 tpres 6466 fntpb 6473 bpoly3 14789 cnfldfunALT 19759 gausslemma2dlem0i 25089 2lgsoddprm 25141 nb3grprlem1 26282 frgr3vlem1 27137 frgr3vlem2 27138 prodtp 29573 hgt750lemb 30734 brtp 31639 sltsolem1 31826 fmtno4prmfac 41484 |
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