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Mirrors > Home > MPE Home > Th. List > elpr2 | Structured version Visualization version Unicode version |
Description: A member of an unordered pair of classes is one or the other of them. Exercise 1 of [TakeutiZaring] p. 15. (Contributed by NM, 14-Oct-2005.) (Proof shortened by JJ, 23-Jul-2021.) |
Ref | Expression |
---|---|
elpr2.1 | |
elpr2.2 |
Ref | Expression |
---|---|
elpr2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3212 | . 2 | |
2 | elpr2.1 | . . . 4 | |
3 | eleq1 2689 | . . . 4 | |
4 | 2, 3 | mpbiri 248 | . . 3 |
5 | elpr2.2 | . . . 4 | |
6 | eleq1 2689 | . . . 4 | |
7 | 5, 6 | mpbiri 248 | . . 3 |
8 | 4, 7 | jaoi 394 | . 2 |
9 | elprg 4196 | . 2 | |
10 | 1, 8, 9 | pm5.21nii 368 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wo 383 wceq 1483 wcel 1990 cvv 3200 cpr 4179 |
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-un 3579 df-sn 4178 df-pr 4180 |
This theorem is referenced by: elopg 4934 elxr 11950 fprodex01 29571 nofv 31810 |
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