Theorem axc4i 2314

Description: Inference version of axc4 2313. (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 2146	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2204	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1537

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 1911  ax-6 1969  ax-7 2009  ax-10 2135  ax-12 2169

This theorem depends on definitions:  df-bi 206  df-or 846  df-ex 1780  df-nf 1784

This theorem is referenced by:  hbae  2429  hbsb2  2484  hbsb2a  2486  hbsb2e  2488  nfabdwOLD  2929  reu6  3666  ralidm  4448  axunndlem1  10397  axacndlem3  10411  axacndlem5  10413  axacnd  10414  bj-nfs1t  35017  bj-hbs1  35039  bj-hbsb2av  35041  bj-hbaeb2  35045  wl-hbae1  35722  frege93  41602  spALT  41850  pm11.57  42045  pm11.59  42047  axc5c4c711toc7  42060  axc11next  42062  hbalg  42213  ax6e2eq  42215  ax6e2eqVD  42565  ichnfimlem  44973