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Mirrors > Home > NFE Home > Th. List > nfrd | GIF version |
Description: Consequence of the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfrd.1 | ⊢ (φ → Ⅎxψ) |
Ref | Expression |
---|---|
nfrd | ⊢ (φ → (ψ → ∀xψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfrd.1 | . 2 ⊢ (φ → Ⅎxψ) | |
2 | nfr 1761 | . 2 ⊢ (Ⅎxψ → (ψ → ∀xψ)) | |
3 | 1, 2 | syl 15 | 1 ⊢ (φ → (ψ → ∀xψ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 Ⅎwnf 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-11 1746 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-nf 1545 |
This theorem is referenced by: alrimdd 1768 nfim1 1811 nfim1OLD 1812 hbimd 1815 nfald 1852 19.9tOLD 1857 19.21tOLD 1863 nfan1 1881 cbv1 1979 cbv2 1981 sbied 2036 sbal1 2126 abidnf 3005 |
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