Theorem axc4i 2320

Description: Inference version of axc4 2319. (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 2210	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1534

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-10 2138  ax-12 2174

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1776  df-nf 1780

This theorem is referenced by:  hbae  2433  hbsb2  2484  hbsb2a  2486  hbsb2e  2488  reu6  3734  ralidm  4517  axunndlem1  10632  axacndlem3  10646  axacndlem5  10648  axacnd  10649  bj-nfs1t  36772  bj-hbs1  36794  bj-hbsb2av  36796  bj-hbaeb2  36800  wl-hbae1  37499  frege93  43945  spALT  44190  pm11.57  44384  pm11.59  44386  axc5c4c711toc7  44399  axc11next  44401  hbalg  44552  ax6e2eq  44554  ax6e2eqVD  44904  ichnfimlem  47387