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Theorem axc4i 2274
Description: Inference version of axc4 2273. (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 2173 . 2 𝑥𝑥𝜑
2 axc4i.1 . 2 (∀𝑥𝜑𝜓)
31, 2alrimi 2225 1 (∀𝑥𝜑 → ∀𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1626
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1867  ax-4 1882  ax-5 1984  ax-6 2050  ax-7 2086  ax-10 2164  ax-12 2192
This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1850  df-nf 1855
This theorem is referenced by:  hbae  2453  hbsb2  2492  hbsb2a  2494  hbsb2e  2496  reu6  3532  axunndlem1  9605  axacndlem3  9619  axacndlem5  9621  axacnd  9622  bj-nfs1t  33016  bj-hbs1  33060  bj-hbsb2av  33062  bj-hbaeb2  33107  wl-hbae1  33612  frege93  38748  pm11.57  39087  pm11.59  39089  axc5c4c711toc7  39103  axc11next  39105  hbalg  39269  ax6e2eq  39271  ax6e2eqVD  39638
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