Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > rmoxfrdOLD | Structured version Visualization version Unicode version |
Description: Transfer "at most one" restricted quantification from a variable to another variable contained in expression . (Contributed by Thierry Arnoux, 7-Apr-2017.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
rmoxfrd.1 | |
rmoxfrd.2 | |
rmoxfrd.3 |
Ref | Expression |
---|---|
rmoxfrdOLD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rmoxfrd.1 | . . . . 5 | |
2 | rmoxfrd.2 | . . . . . 6 | |
3 | reurex 3160 | . . . . . 6 | |
4 | 2, 3 | syl 17 | . . . . 5 |
5 | rmoxfrd.3 | . . . . 5 | |
6 | 1, 4, 5 | rexxfrd 4881 | . . . 4 |
7 | df-rex 2918 | . . . 4 | |
8 | df-rex 2918 | . . . 4 | |
9 | 6, 7, 8 | 3bitr3g 302 | . . 3 |
10 | 1, 2, 5 | reuxfr4d 29330 | . . . 4 |
11 | df-reu 2919 | . . . 4 | |
12 | df-reu 2919 | . . . 4 | |
13 | 10, 11, 12 | 3bitr3g 302 | . . 3 |
14 | 9, 13 | imbi12d 334 | . 2 |
15 | df-mo 2475 | . 2 | |
16 | df-mo 2475 | . 2 | |
17 | 14, 15, 16 | 3bitr4g 303 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 weu 2470 wmo 2471 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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-reu 2919 df-rmo 2920 df-v 3202 |
This theorem is referenced by: (None) |
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