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Theorem axc4i 2321
Description: Inference version of axc4 2320. (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 2152 . 2 𝑥𝑥𝜑
2 axc4i.1 . 2 (∀𝑥𝜑𝜓)
31, 2alrimi 2211 1 (∀𝑥𝜑 → ∀𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-10 2141  ax-12 2175
This theorem depends on definitions:  df-bi 210  df-or 848  df-ex 1788  df-nf 1792
This theorem is referenced by:  hbae  2430  hbsb2  2485  hbsb2a  2487  hbsb2e  2489  nfabdwOLD  2928  reu6  3639  ralidm  4423  axunndlem1  10209  axacndlem3  10223  axacndlem5  10225  axacnd  10226  bj-nfs1t  34709  bj-hbs1  34731  bj-hbsb2av  34733  bj-hbaeb2  34738  wl-hbae1  35415  frege93  41241  spALT  41490  pm11.57  41680  pm11.59  41682  axc5c4c711toc7  41695  axc11next  41697  hbalg  41848  ax6e2eq  41850  ax6e2eqVD  42200  ichnfimlem  44588
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