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Mirrors > Home > MPE Home > Th. List > ralxfrd2 | Structured version Visualization version Unicode version |
Description: Transfer universal quantification from a variable to another variable contained in expression . Variant of ralxfrd 4879. (Contributed by Alexander van der Vekens, 25-Apr-2018.) |
Ref | Expression |
---|---|
ralxfrd2.1 | |
ralxfrd2.2 | |
ralxfrd2.3 |
Ref | Expression |
---|---|
ralxfrd2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralxfrd2.1 | . . . 4 | |
2 | ralxfrd2.3 | . . . . 5 | |
3 | 2 | 3expa 1265 | . . . 4 |
4 | 1, 3 | rspcdv 3312 | . . 3 |
5 | 4 | ralrimdva 2969 | . 2 |
6 | ralxfrd2.2 | . . . 4 | |
7 | r19.29 3072 | . . . . 5 | |
8 | 2 | ad4ant134 1296 | . . . . . . . . 9 |
9 | 8 | exbiri 652 | . . . . . . . 8 |
10 | 9 | com23 86 | . . . . . . 7 |
11 | 10 | impd 447 | . . . . . 6 |
12 | 11 | rexlimdva 3031 | . . . . 5 |
13 | 7, 12 | syl5 34 | . . . 4 |
14 | 6, 13 | mpan2d 710 | . . 3 |
15 | 14 | ralrimdva 2969 | . 2 |
16 | 5, 15 | impbid 202 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 wral 2912 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-3an 1039 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-ral 2917 df-rex 2918 df-v 3202 |
This theorem is referenced by: rexxfrd2 4885 ntrclsiso 38365 ntrclsk2 38366 ntrclskb 38367 ntrclsk3 38368 ntrclsk13 38369 ntrclsk4 38370 |
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