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Mirrors > Home > MPE Home > Th. List > ifpr | Structured version Visualization version 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 3212 | . 2 | |
2 | elex 3212 | . 2 | |
3 | ifcl 4130 | . . 3 | |
4 | ifeqor 4132 | . . . 4 | |
5 | elprg 4196 | . . . 4 | |
6 | 4, 5 | mpbiri 248 | . . 3 |
7 | 3, 6 | syl 17 | . 2 |
8 | 1, 2, 7 | syl2an 494 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wo 383 wa 384 wceq 1483 wcel 1990 cvv 3200 cif 4086 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-if 4087 df-sn 4178 df-pr 4180 |
This theorem is referenced by: suppr 8377 infpr 8409 uvcvvcl 20126 indf 30077 |
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