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Mirrors > Home > NFE Home > Th. List > nfcvf | Unicode version |
Description: If and are distinct, then is not free in . (Contributed by Mario Carneiro, 8-Oct-2016.) |
Ref | Expression |
---|---|
nfcvf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2489 | . 2 | |
2 | nfcv 2489 | . 2 | |
3 | id 19 | . 2 | |
4 | 1, 2, 3 | dvelimc 2510 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wal 1540 wceq 1642 wnfc 2476 |
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-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-cleq 2346 df-clel 2349 df-nfc 2478 |
This theorem is referenced by: nfcvf2 2512 nfrald 2665 ralcom2 2775 nfreud 2783 nfrmod 2784 nfrmo 2786 nfiotad 4342 |
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