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Theorem nf5rd 2228
Description: Consequence of the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nf5rd.1 (𝜑 → Ⅎ𝑥𝜓)
Assertion
Ref Expression
nf5rd (𝜑 → (𝜓 → ∀𝑥𝜓))

Proof of Theorem nf5rd
StepHypRef Expression
1 nf5rd.1 . 2 (𝜑 → Ⅎ𝑥𝜓)
2 nf5r 2226 . 2 (Ⅎ𝑥𝜓 → (𝜓 → ∀𝑥𝜓))
31, 2syl 17 1 (𝜑 → (𝜓 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1650  wnf 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-12 2211
This theorem depends on definitions:  df-bi 198  df-ex 1875  df-nf 1879
This theorem is referenced by:  alrimdd  2247  nf5di  2295  hbimd  2303  hbnt  2320  dvelimhw  2340  spimed  2361  cbv2  2375  dveeq2  2398  dveeq1  2400  axc9  2402  dvelimh  2430  abidnf  3534  eusvnfb  5030  axrepnd  9673  axacndlem4  9689  bj-spimedv  33175  bj-cbv2v  33187  wl-nfeqfb  33769
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