Theorem axc4i 2357

Description: Inference version of axc4 2356. (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 2188	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2251	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1561

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-10 2178  ax-12 2215

This theorem depends on definitions:  df-bi 210  df-or 861  df-ex 1803  df-nf 1807

This theorem is referenced by:  hbae  2465  hbsb2  2516  hbsb2a  2518  hbsb2e  2520  reu6  3692  ralidm  4474  axunndlem1  10568  axacndlem3  10582  axacndlem5  10584  axacnd  10585  bj-nfs1t  37282  bj-hbs1  37304  bj-hbsb2av  37306  bj-hbaeb2  37310  wl-hbae1  38029  frege93  44539  spALT  44784  pm11.57  44958  pm11.59  44960  axc5c4c711toc7  44973  axc11next  44975  hbalg  45123  ax6e2eq  45125  ax6e2eqVD  45474  ichnfimlem  48068