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Mirrors > Home > MPE Home > Th. List > iota2df | Structured version Visualization version Unicode version |
Description: A condition that allows us to represent "the unique element such that " with a class expression . (Contributed by NM, 30-Dec-2014.) |
Ref | Expression |
---|---|
iota2df.1 | |
iota2df.2 | |
iota2df.3 | |
iota2df.4 | |
iota2df.5 | |
iota2df.6 |
Ref | Expression |
---|---|
iota2df |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iota2df.1 | . 2 | |
2 | iota2df.3 | . . 3 | |
3 | simpr 477 | . . . 4 | |
4 | 3 | eqeq2d 2632 | . . 3 |
5 | 2, 4 | bibi12d 335 | . 2 |
6 | iota2df.2 | . . 3 | |
7 | iota1 5865 | . . 3 | |
8 | 6, 7 | syl 17 | . 2 |
9 | iota2df.4 | . 2 | |
10 | iota2df.6 | . 2 | |
11 | iota2df.5 | . . 3 | |
12 | nfiota1 5853 | . . . . 5 | |
13 | 12 | a1i 11 | . . . 4 |
14 | 13, 10 | nfeqd 2772 | . . 3 |
15 | 11, 14 | nfbid 1832 | . 2 |
16 | 1, 5, 8, 9, 10, 15 | vtocldf 3256 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wnf 1708 wcel 1990 weu 2470 wnfc 2751 cio 5849 |
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-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-sbc 3436 df-un 3579 df-sn 4178 df-pr 4180 df-uni 4437 df-iota 5851 |
This theorem is referenced by: iota2d 5876 iota2 5877 riota2df 6631 opiota 7229 |
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