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Mirrors > Home > MPE Home > Th. List > rexcomf | Structured version Visualization version Unicode version |
Description: Commutation of restricted existential quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
ralcomf.1 | |
ralcomf.2 |
Ref | Expression |
---|---|
rexcomf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 466 | . . . . 5 | |
2 | 1 | anbi1i 731 | . . . 4 |
3 | 2 | 2exbii 1775 | . . 3 |
4 | excom 2042 | . . 3 | |
5 | 3, 4 | bitri 264 | . 2 |
6 | ralcomf.1 | . . 3 | |
7 | 6 | r2exf 3060 | . 2 |
8 | ralcomf.2 | . . 3 | |
9 | 8 | r2exf 3060 | . 2 |
10 | 5, 7, 9 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wex 1704 wcel 1990 wnfc 2751 wrex 2913 |
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-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 |
This theorem is referenced by: rexcom 3099 rexcom4f 29317 |
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