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Mirrors > Home > NFE Home > Th. List > nfor | Unicode version |
Description: If is not free in and , it is not free in . (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nf.1 | |
nf.2 |
Ref | Expression |
---|---|
nfor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-or 359 | . 2 | |
2 | nf.1 | . . . 4 | |
3 | 2 | nfn 1793 | . . 3 |
4 | nf.2 | . . 3 | |
5 | 3, 4 | nfim 1813 | . 2 |
6 | 1, 5 | nfxfr 1570 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wo 357 wnf 1544 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-11 1746 |
This theorem depends on definitions: df-bi 177 df-or 359 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: nf3or 1837 axi12 2333 nfpr 3773 |
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