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Theorem axc4i 2295
Description: Inference version of axc4 2294. (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 2184 . 2 𝑥𝑥𝜑
2 axc4i.1 . 2 (∀𝑥𝜑𝜓)
31, 2alrimi 2238 1 (∀𝑥𝜑 → ∀𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-or 837  df-ex 1853  df-nf 1858
This theorem is referenced by:  hbae  2467  hbsb2  2506  hbsb2a  2508  hbsb2e  2510  reu6  3547  axunndlem1  9619  axacndlem3  9633  axacndlem5  9635  axacnd  9636  bj-nfs1t  33051  bj-hbs1  33094  bj-hbsb2av  33096  bj-hbaeb2  33140  wl-hbae1  33640  frege93  38776  pm11.57  39115  pm11.59  39117  axc5c4c711toc7  39131  axc11next  39133  hbalg  39296  ax6e2eq  39298  ax6e2eqVD  39665
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