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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 4383. (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 2785 | . . . . 5 |
4 | 1, 3 | syl 14 | . . . 4 |
5 | 4 | com12 30 | . . 3 |
6 | 5 | ralrimiv 2504 | . 2 |
7 | ralxfr.2 | . . . 4 | |
8 | nfra1 2466 | . . . . 5 | |
9 | nfv 1508 | . . . . 5 | |
10 | rsp 2480 | . . . . . 6 | |
11 | 2 | biimprcd 159 | . . . . . 6 |
12 | 10, 11 | syl6 33 | . . . . 5 |
13 | 8, 9, 12 | rexlimd 2546 | . . . 4 |
14 | 7, 13 | syl5 32 | . . 3 |
15 | 14 | ralrimiv 2504 | . 2 |
16 | 6, 15 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 wcel 1480 wral 2416 wrex 2417 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 |
This theorem is referenced by: (None) |
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