Theorem axc4i 2322

Description: Inference version of axc4 2321. (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 2151	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2213	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-10 2141  ax-12 2177

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1780  df-nf 1784

This theorem is referenced by:  hbae  2435  hbsb2  2486  hbsb2a  2488  hbsb2e  2490  reu6  3709  ralidm  4487  axunndlem1  10609  axacndlem3  10623  axacndlem5  10625  axacnd  10626  bj-nfs1t  36808  bj-hbs1  36830  bj-hbsb2av  36832  bj-hbaeb2  36836  wl-hbae1  37537  frege93  43980  spALT  44225  pm11.57  44413  pm11.59  44415  axc5c4c711toc7  44428  axc11next  44430  hbalg  44580  ax6e2eq  44582  ax6e2eqVD  44931  ichnfimlem  47477