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Theorem axc4i 2330
 Description: Inference version of axc4 2329. (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 1536 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-12 2175 This theorem depends on definitions:  df-bi 210  df-or 845  df-ex 1782  df-nf 1786 This theorem is referenced by:  hbae  2442  hbsb2  2500  hbsb2a  2502  hbsb2e  2504  hbsb2ALT  2575  nfabdw  2976  reu6  3666  axunndlem1  10021  axacndlem3  10035  axacndlem5  10037  axacnd  10038  bj-nfs1t  34294  bj-hbs1  34316  bj-hbsb2av  34318  bj-hbaeb2  34323  wl-hbae1  34991  frege93  40744  spALT  40994  pm11.57  41180  pm11.59  41182  axc5c4c711toc7  41195  axc11next  41197  hbalg  41348  ax6e2eq  41350  ax6e2eqVD  41700  ichnfimlem  44064
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