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Mirrors > Home > ILE Home > Th. List > nfvd | GIF version |
Description: nfv 1509 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1565. (Contributed by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
nfvd | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1509 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | 1 | a1i 9 | 1 ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1437 |
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-gen 1426 ax-17 1507 |
This theorem depends on definitions: df-bi 116 df-nf 1438 |
This theorem is referenced by: sbiedv 1763 cbvaldva 1901 cbvexdva 1902 vtocld 2741 sbcied 2949 nfunid 3751 peano2 4517 iota2d 5121 iota2 5122 riota5f 5762 mpoxopoveq 6145 bdsepnft 13256 |
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