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Mirrors > Home > ILE Home > Th. List > nfand | Unicode version |
Description: If in a context is not free in and , it is not free in . (Contributed by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
nfand.1 | |
nfand.2 |
Ref | Expression |
---|---|
nfand |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfand.1 | . . . 4 | |
2 | nfand.2 | . . . 4 | |
3 | 1, 2 | jca 304 | . . 3 |
4 | df-nf 1454 | . . . . . 6 | |
5 | df-nf 1454 | . . . . . 6 | |
6 | 4, 5 | anbi12i 457 | . . . . 5 |
7 | 19.26 1474 | . . . . 5 | |
8 | 6, 7 | bitr4i 186 | . . . 4 |
9 | anim12 342 | . . . . . 6 | |
10 | 19.26 1474 | . . . . . 6 | |
11 | 9, 10 | syl6ibr 161 | . . . . 5 |
12 | 11 | alimi 1448 | . . . 4 |
13 | 8, 12 | sylbi 120 | . . 3 |
14 | 3, 13 | syl 14 | . 2 |
15 | df-nf 1454 | . 2 | |
16 | 14, 15 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1346 wnf 1453 |
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 1440 ax-gen 1442 |
This theorem depends on definitions: df-bi 116 df-nf 1454 |
This theorem is referenced by: nf3and 1562 nfbid 1581 nfsbxy 1935 nfsbxyt 1936 nfeld 2328 nfrexdxy 2504 nfreudxy 2643 nfifd 3553 nfriotadxy 5817 bdsepnft 13922 strcollnft 14019 |
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