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Mirrors > Home > ILE Home > Th. List > alxfr | Unicode version |
Description: Transfer universal quantification from a variable to another variable contained in expression . (Contributed by NM, 18-Feb-2007.) |
Ref | Expression |
---|---|
alxfr.1 |
Ref | Expression |
---|---|
alxfr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alxfr.1 | . . . . . . 7 | |
2 | 1 | spcgv 2685 | . . . . . 6 |
3 | 2 | com12 30 | . . . . 5 |
4 | 3 | alimdv 1800 | . . . 4 |
5 | 4 | com12 30 | . . 3 |
6 | 5 | adantr 270 | . 2 |
7 | nfa1 1474 | . . . . . 6 | |
8 | nfv 1461 | . . . . . 6 | |
9 | sp 1441 | . . . . . . 7 | |
10 | 9, 1 | syl5ibrcom 155 | . . . . . 6 |
11 | 7, 8, 10 | exlimd 1528 | . . . . 5 |
12 | 11 | alimdv 1800 | . . . 4 |
13 | 12 | com12 30 | . . 3 |
14 | 13 | adantl 271 | . 2 |
15 | 6, 14 | impbid 127 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wceq 1284 wex 1421 wcel 1433 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 |
This theorem is referenced by: (None) |
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