Theorem axc4i 2331

Description: Inference version of axc4 2330. (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 2162	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2225	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1545

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-10 2152  ax-12 2189

This theorem depends on definitions:  df-bi 208  df-or 854  df-ex 1787  df-nf 1791

This theorem is referenced by:  hbae  2439  hbsb2  2490  hbsb2a  2492  hbsb2e  2494  reu6  3674  ralidm  4452  axunndlem1  10516  axacndlem3  10530  axacndlem5  10532  axacnd  10533  bj-nfs1t  37150  bj-hbs1  37172  bj-hbsb2av  37174  bj-hbaeb2  37178  wl-hbae1  37897  frege93  44407  spALT  44652  pm11.57  44840  pm11.59  44842  axc5c4c711toc7  44855  axc11next  44857  hbalg  45006  ax6e2eq  45008  ax6e2eqVD  45357  ichnfimlem  47945