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Mirrors > Home > MPE Home > Th. List > nfvd | Structured version Visualization version GIF version |
Description: nfv 1830 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1812. (Contributed by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
nfvd | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1830 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | 1 | a1i 11 | 1 ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 Ⅎwnf 1699 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-5 1827 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nf 1701 |
This theorem is referenced by: cbvald 2265 cbvaldvaOLD 2270 cbvexdvaOLD 2272 sbiedv 2398 vtocld 3230 sbcied 3439 nfunid 4379 iota2d 5793 iota2 5794 riota5f 6535 opiota 7118 mpt2xopoveq 7232 axrepndlem1 9293 axunndlem1 9296 fproddivf 14557 xrofsup 28923 bj-cbvaldvav 31928 bj-cbvexdvav 31929 wl-mo2t 32536 wl-sb8eut 32538 riotasv2d 33261 cdleme42b 34784 dihvalcqpre 35542 mapdheq 36035 hdmap1eq 36109 hdmapval2lem 36141 |
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