Theorem axc4i 2322

Description: Inference version of axc4 2321. (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 2151	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2213	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1538

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 1910  ax-6 1967  ax-7 2007  ax-10 2141  ax-12 2177

This theorem depends on definitions:  df-bi 207  df-or 849  df-ex 1780  df-nf 1784

This theorem is referenced by:  hbae  2436  hbsb2  2487  hbsb2a  2489  hbsb2e  2491  reu6  3732  ralidm  4512  axunndlem1  10635  axacndlem3  10649  axacndlem5  10651  axacnd  10652  bj-nfs1t  36791  bj-hbs1  36813  bj-hbsb2av  36815  bj-hbaeb2  36819  wl-hbae1  37520  frege93  43969  spALT  44214  pm11.57  44408  pm11.59  44410  axc5c4c711toc7  44423  axc11next  44425  hbalg  44575  ax6e2eq  44577  ax6e2eqVD  44927  ichnfimlem  47450