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Mirrors > Home > MPE Home > Th. List > tpid1 | Structured version Visualization version Unicode version |
Description: One of the three elements of an unordered triple. (Contributed by NM, 7-Apr-1994.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
tpid1.1 |
Ref | Expression |
---|---|
tpid1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2622 | . . 3 | |
2 | 1 | 3mix1i 1233 | . 2 |
3 | tpid1.1 | . . 3 | |
4 | 3 | eltp 4230 | . 2 |
5 | 2, 4 | mpbir 221 | 1 |
Colors of variables: wff setvar class |
Syntax hints: 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: tpnz 4313 wrdl3s3 13705 cffldtocusgr 26343 umgrwwlks2on 26850 sgnsf 29729 sgncl 30600 prodfzo03 30681 circlevma 30720 circlemethhgt 30721 hgt750lemg 30732 hgt750lemb 30734 hgt750lema 30735 hgt750leme 30736 tgoldbachgtde 30738 tgoldbachgt 30741 kur14lem7 31194 kur14lem9 31196 brtpid1 31602 rabren3dioph 37379 fourierdlem102 40425 fourierdlem114 40437 etransclem48 40499 |
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