Theorem axc4i 2355

Description: Inference version of axc4 2354. (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 2186	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2249	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1568

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-10 2176  ax-12 2213

This theorem depends on definitions:  df-bi 210  df-or 861  df-ex 1810  df-nf 1814

This theorem is referenced by:  hbae  2463  hbsb2  2514  hbsb2a  2516  hbsb2e  2518  reu6  3690  ralidm  4479  axunndlem1  10581  axacndlem3  10595  axacndlem5  10597  axacnd  10598  bj-nfs1t  37406  bj-hbs1  37428  bj-hbsb2av  37430  bj-hbaeb2  37434  wl-hbae1  38155  frege93  44665  spALT  44910  pm11.57  45082  pm11.59  45084  axc5c4c711toc7  45097  axc11next  45099  hbalg  45247  ax6e2eq  45249  ax6e2eqVD  45598  ichnfimlem  48195