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Mirrors > Home > ILE Home > Th. List > nfnt | Unicode version |
Description: If is not free in , then it is not free in . (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 28-Dec-2017.) (Revised by BJ, 24-Jul-2019.) |
Ref | Expression |
---|---|
nfnt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnf1 1508 | . 2 | |
2 | df-nf 1422 | . . 3 | |
3 | hbnt 1616 | . . 3 | |
4 | 2, 3 | sylbi 120 | . 2 |
5 | 1, 4 | nfd 1488 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wal 1314 wnf 1421 |
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-in1 588 ax-in2 589 ax-5 1408 ax-gen 1410 ax-ie2 1455 ax-4 1472 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 df-nf 1422 |
This theorem is referenced by: nfnd 1620 nfn 1621 |
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