Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ralxfrd | Unicode version |
Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by NM, 15-Aug-2014.) (Proof shortened by Mario Carneiro, 19-Nov-2016.) |
Ref | Expression |
---|---|
ralxfrd.1 | |
ralxfrd.2 | |
ralxfrd.3 |
Ref | Expression |
---|---|
ralxfrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralxfrd.1 | . . . 4 | |
2 | ralxfrd.3 | . . . . 5 | |
3 | 2 | adantlr 474 | . . . 4 |
4 | 1, 3 | rspcdv 2837 | . . 3 |
5 | 4 | ralrimdva 2550 | . 2 |
6 | ralxfrd.2 | . . . 4 | |
7 | r19.29 2607 | . . . . 5 | |
8 | 2 | biimprd 157 | . . . . . . . . 9 |
9 | 8 | expimpd 361 | . . . . . . . 8 |
10 | 9 | ancomsd 267 | . . . . . . 7 |
11 | 10 | ad2antrr 485 | . . . . . 6 |
12 | 11 | rexlimdva 2587 | . . . . 5 |
13 | 7, 12 | syl5 32 | . . . 4 |
14 | 6, 13 | mpan2d 426 | . . 3 |
15 | 14 | ralrimdva 2550 | . 2 |
16 | 5, 15 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wcel 2141 wral 2448 wrex 2449 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 |
This theorem is referenced by: ralxfr2d 4447 ralxfr 4449 |
Copyright terms: Public domain | W3C validator |