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Theorem axc4i 2116
 Description: Inference version of axc4 2115. (Contributed by NM, 3-Jan-1993.)
Hypothesis
Ref Expression
axc4i.1 (∀𝑥𝜑𝜓)
Assertion
Ref Expression
axc4i (∀𝑥𝜑 → ∀𝑥𝜓)

Proof of Theorem axc4i
StepHypRef Expression
1 nfa1 2015 . 2 𝑥𝑥𝜑
2 axc4i.1 . 2 (∀𝑥𝜑𝜓)
31, 2alrimi 2069 1 (∀𝑥𝜑 → ∀𝑥𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1473 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701 This theorem is referenced by:  hbae  2303  hbsb2  2347  hbsb2a  2349  hbsb2e  2351  reu6  3362  axunndlem1  9296  axacndlem3  9310  axacndlem5  9312  axacnd  9313  bj-nfs1t  31901  bj-hbs1  31946  bj-hbsb2av  31948  bj-hbaeb2  31993  wl-hbae1  32482  frege93  37270  pm11.57  37611  pm11.59  37613  axc5c4c711toc7  37627  axc11next  37629  hbalg  37792  ax6e2eq  37794  ax6e2eqVD  38165
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