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Mirrors > Home > NFE Home > Th. List > ifpr | Unicode version |
Description: Membership of a conditional operator in an unordered pair. (Contributed by NM, 17-Jun-2007.) |
Ref | Expression |
---|---|
ifpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2867 | . 2 | |
2 | elex 2867 | . 2 | |
3 | ifcl 3698 | . . 3 | |
4 | ifeqor 3699 | . . . 4 | |
5 | elprg 3750 | . . . 4 | |
6 | 4, 5 | mpbiri 224 | . . 3 |
7 | 3, 6 | syl 15 | . 2 |
8 | 1, 2, 7 | syl2an 463 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wo 357 wa 358 wceq 1642 wcel 1710 cvv 2859 cif 3662 cpr 3738 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-if 3663 df-sn 3741 df-pr 3742 |
This theorem is referenced by: (None) |
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