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Mirrors > Home > ILE Home > Th. List > nf4r | Unicode version |
Description: If is always true or always false, then variable is effectively not free in . The converse holds given a decidability condition, as seen at nf4dc 1648. (Contributed by Jim Kingdon, 21-Jul-2018.) |
Ref | Expression |
---|---|
nf4r |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 717 | . . 3 | |
2 | alnex 1475 | . . . 4 | |
3 | 2 | orbi2i 751 | . . 3 |
4 | 1, 3 | bitr4i 186 | . 2 |
5 | imorr 710 | . . 3 | |
6 | nf2 1646 | . . 3 | |
7 | 5, 6 | sylibr 133 | . 2 |
8 | 4, 7 | sylbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wo 697 wal 1329 wnf 1436 wex 1468 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-gen 1425 ax-ie2 1470 ax-4 1487 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 |
This theorem is referenced by: (None) |
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