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Mirrors > Home > MPE Home > Th. List > dmtpop | Structured version Visualization version Unicode version |
Description: The domain of an unordered triple of ordered pairs. (Contributed by NM, 14-Sep-2011.) |
Ref | Expression |
---|---|
dmsnop.1 | |
dmprop.1 | |
dmtpop.1 |
Ref | Expression |
---|---|
dmtpop |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-tp 4182 | . . . 4 | |
2 | 1 | dmeqi 5325 | . . 3 |
3 | dmun 5331 | . . 3 | |
4 | dmsnop.1 | . . . . 5 | |
5 | dmprop.1 | . . . . 5 | |
6 | 4, 5 | dmprop 5610 | . . . 4 |
7 | dmtpop.1 | . . . . 5 | |
8 | 7 | dmsnop 5609 | . . . 4 |
9 | 6, 8 | uneq12i 3765 | . . 3 |
10 | 2, 3, 9 | 3eqtri 2648 | . 2 |
11 | df-tp 4182 | . 2 | |
12 | 10, 11 | eqtr4i 2647 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wcel 1990 cvv 3200 cun 3572 csn 4177 cpr 4179 ctp 4181 cop 4183 cdm 5114 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 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-tp 4182 df-op 4184 df-br 4654 df-dm 5124 |
This theorem is referenced by: fntp 5949 fntpb 6473 cnfldfun 19758 |
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