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Mirrors > Home > ILE Home > Th. List > nf3an | Unicode version |
Description: If is not free in , , and , it is not free in . (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfan.1 | |
nfan.2 | |
nfan.3 |
Ref | Expression |
---|---|
nf3an |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 964 | . 2 | |
2 | nfan.1 | . . . 4 | |
3 | nfan.2 | . . . 4 | |
4 | 2, 3 | nfan 1544 | . . 3 |
5 | nfan.3 | . . 3 | |
6 | 4, 5 | nfan 1544 | . 2 |
7 | 1, 6 | nfxfr 1450 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 w3a 962 wnf 1436 |
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-5 1423 ax-gen 1425 ax-4 1487 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-nf 1437 |
This theorem is referenced by: vtocl3gaf 2750 mob 2861 nfop 3716 mkvprop 7025 seq3f1olemstep 10267 seq3f1olemp 10268 nfsum1 11118 nfsum 11119 |
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