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Mirrors > Home > MPE Home > Th. List > reu7 | Structured version Visualization version Unicode version |
Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.) |
Ref | Expression |
---|---|
rmo4.1 |
Ref | Expression |
---|---|
reu7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reu3 3396 | . 2 | |
2 | rmo4.1 | . . . . . . 7 | |
3 | equequ1 1952 | . . . . . . . 8 | |
4 | equcom 1945 | . . . . . . . 8 | |
5 | 3, 4 | syl6bb 276 | . . . . . . 7 |
6 | 2, 5 | imbi12d 334 | . . . . . 6 |
7 | 6 | cbvralv 3171 | . . . . 5 |
8 | 7 | rexbii 3041 | . . . 4 |
9 | equequ1 1952 | . . . . . . 7 | |
10 | 9 | imbi2d 330 | . . . . . 6 |
11 | 10 | ralbidv 2986 | . . . . 5 |
12 | 11 | cbvrexv 3172 | . . . 4 |
13 | 8, 12 | bitri 264 | . . 3 |
14 | 13 | anbi2i 730 | . 2 |
15 | 1, 14 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wral 2912 wrex 2913 wreu 2914 |
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-eu 2474 df-mo 2475 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-reu 2919 df-rmo 2920 |
This theorem is referenced by: cshwrepswhash1 15809 |
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