Theorem axc4i 2353

Description: Inference version of axc4 2352. (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 2184	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2247	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1557

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-10 2174  ax-12 2211

This theorem depends on definitions:  df-bi 209  df-or 859  df-ex 1799  df-nf 1803

This theorem is referenced by:  hbae  2461  hbsb2  2512  hbsb2a  2514  hbsb2e  2516  reu6  3687  ralidm  4468  axunndlem1  10546  axacndlem3  10560  axacndlem5  10562  axacnd  10563  bj-nfs1t  37235  bj-hbs1  37257  bj-hbsb2av  37259  bj-hbaeb2  37263  wl-hbae1  37982  frege93  44492  spALT  44737  pm11.57  44925  pm11.59  44927  axc5c4c711toc7  44940  axc11next  44942  hbalg  45091  ax6e2eq  45093  ax6e2eqVD  45442  ichnfimlem  48029