Theorem axc4i 2127

Description: Inference version of axc4 2126. (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 2025	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2080	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1478

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1702  df-nf 1707

This theorem is referenced by:  hbae  2314  hbsb2  2358  hbsb2a  2360  hbsb2e  2362  reu6  3377  axunndlem1  9361  axacndlem3  9375  axacndlem5  9377  axacnd  9378  bj-nfs1t  32353  bj-hbs1  32398  bj-hbsb2av  32400  bj-hbaeb2  32445  wl-hbae1  32932  frege93  37729  pm11.57  38068  pm11.59  38070  axc5c4c711toc7  38084  axc11next  38086  hbalg  38250  ax6e2eq  38252  ax6e2eqVD  38623