Theorem axc4i 2316

Description: Inference version of axc4 2315. (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 2149	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2207	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-10 2138  ax-12 2172

This theorem depends on definitions:  df-bi 206  df-or 847  df-ex 1783  df-nf 1787

This theorem is referenced by:  hbae  2431  hbsb2  2482  hbsb2a  2484  hbsb2e  2486  nfabdwOLD  2928  reu6  3723  ralidm  4512  axunndlem1  10590  axacndlem3  10604  axacndlem5  10606  axacnd  10607  bj-nfs1t  35668  bj-hbs1  35690  bj-hbsb2av  35692  bj-hbaeb2  35696  wl-hbae1  36388  frege93  42707  spALT  42953  pm11.57  43148  pm11.59  43150  axc5c4c711toc7  43163  axc11next  43165  hbalg  43316  ax6e2eq  43318  ax6e2eqVD  43668  ichnfimlem  46131