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Mirrors > Home > ILE Home > Th. List > ralxfrALT | Unicode version |
Description: Transfer universal quantification from a variable to another variable contained in expression . This proof does not use ralxfrd 4194. (Contributed by NM, 10-Jun-2005.) (Revised by Mario Carneiro, 15-Aug-2014.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ralxfr.1 | |
ralxfr.2 | |
ralxfr.3 |
Ref | Expression |
---|---|
ralxfrALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralxfr.1 | . . . . 5 | |
2 | ralxfr.3 | . . . . . 6 | |
3 | 2 | rspcv 2652 | . . . . 5 |
4 | 1, 3 | syl 14 | . . . 4 |
5 | 4 | com12 27 | . . 3 |
6 | 5 | ralrimiv 2391 | . 2 |
7 | ralxfr.2 | . . . 4 | |
8 | nfra1 2355 | . . . . 5 | |
9 | nfv 1421 | . . . . 5 | |
10 | rsp 2369 | . . . . . 6 | |
11 | 2 | biimprcd 149 | . . . . . 6 |
12 | 10, 11 | syl6 29 | . . . . 5 |
13 | 8, 9, 12 | rexlimd 2430 | . . . 4 |
14 | 7, 13 | syl5 28 | . . 3 |
15 | 14 | ralrimiv 2391 | . 2 |
16 | 6, 15 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 wral 2306 wrex 2307 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 |
This theorem is referenced by: (None) |
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