Theorem axc4i 2315

Description: Inference version of axc4 2314. (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 2148	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2206	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1539

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-10 2137  ax-12 2171

This theorem depends on definitions:  df-bi 206  df-or 846  df-ex 1782  df-nf 1786

This theorem is referenced by:  hbae  2429  hbsb2  2480  hbsb2a  2482  hbsb2e  2484  nfabdwOLD  2926  reu6  3718  ralidm  4505  axunndlem1  10572  axacndlem3  10586  axacndlem5  10588  axacnd  10589  bj-nfs1t  35470  bj-hbs1  35492  bj-hbsb2av  35494  bj-hbaeb2  35498  wl-hbae1  36190  frege93  42476  spALT  42722  pm11.57  42917  pm11.59  42919  axc5c4c711toc7  42932  axc11next  42934  hbalg  43085  ax6e2eq  43087  ax6e2eqVD  43437  ichnfimlem  45901