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Mirrors > Home > MPE Home > Th. List > dftr2 | Structured version Visualization version Unicode version |
Description: An alternate way of defining a transitive class. Exercise 7 of [TakeutiZaring] p. 40. (Contributed by NM, 24-Apr-1994.) |
Ref | Expression |
---|---|
dftr2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 3591 | . 2 | |
2 | df-tr 4753 | . 2 | |
3 | 19.23v 1902 | . . . 4 | |
4 | eluni 4439 | . . . . 5 | |
5 | 4 | imbi1i 339 | . . . 4 |
6 | 3, 5 | bitr4i 267 | . . 3 |
7 | 6 | albii 1747 | . 2 |
8 | 1, 2, 7 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wex 1704 wcel 1990 wss 3574 cuni 4436 wtr 4752 |
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-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-in 3581 df-ss 3588 df-uni 4437 df-tr 4753 |
This theorem is referenced by: dftr5 4755 trel 4759 ordelord 5745 suctr 5808 suctrOLD 5809 ordom 7074 hartogs 8449 card2on 8459 trcl 8604 tskwe 8776 ondomon 9385 dftr6 31640 elpotr 31686 nosupno 31849 hftr 32289 dford4 37596 tratrb 38746 trsbc 38750 truniALT 38751 sspwtr 39048 sspwtrALT 39049 sspwtrALT2 39058 pwtrVD 39059 pwtrrVD 39060 suctrALT 39061 suctrALT2VD 39071 suctrALT2 39072 tratrbVD 39097 trsbcVD 39113 truniALTVD 39114 trintALTVD 39116 trintALT 39117 suctrALTcf 39158 suctrALTcfVD 39159 suctrALT3 39160 |
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