Theorem axc4i 2116

Description: Inference version of axc4 2115. (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 2015	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2069	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701

This theorem is referenced by:  hbae  2303  hbsb2  2347  hbsb2a  2349  hbsb2e  2351  reu6  3362  axunndlem1  9296  axacndlem3  9310  axacndlem5  9312  axacnd  9313  bj-nfs1t  31901  bj-hbs1  31946  bj-hbsb2av  31948  bj-hbaeb2  31993  wl-hbae1  32482  frege93  37270  pm11.57  37611  pm11.59  37613  axc5c4c711toc7  37627  axc11next  37629  hbalg  37792  ax6e2eq  37794  ax6e2eqVD  38165