Theorem axc4i 2321

Description: Inference version of axc4 2320. (Contributed by NM, 3-Jan-1993.)

Hypothesis

Ref	Expression
axc4i.1	⊢ (∀𝑥𝜑 → 𝜓)

Assertion

Ref	Expression
axc4i	⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Proof of Theorem axc4i

Step	Hyp	Ref	Expression
1		nfa1 2152	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2211	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

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