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Mirrors > Home > MPE Home > Th. List > nf5rd | Structured version Visualization version GIF version |
Description: Consequence of the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nf5rd.1 | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Ref | Expression |
---|---|
nf5rd | ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nf5rd.1 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝜓) | |
2 | nf5r 2187 | . 2 ⊢ (Ⅎ𝑥𝜓 → (𝜓 → ∀𝑥𝜓)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1537 Ⅎwnf 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-12 2171 |
This theorem depends on definitions: df-bi 206 df-ex 1783 df-nf 1787 |
This theorem is referenced by: spimedv 2190 alrimdd 2207 nf5di 2282 hbnt 2291 hbimd 2295 dvelimhw 2343 dveeq2 2378 dveeq1 2380 axc9 2382 spimed 2388 dvelimh 2450 abidnf 3638 eusvnfb 5316 axrepnd 10350 axacndlem4 10366 bj-cbv2v 34980 bj-elgab 35127 wl-nfeqfb 35695 |
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