Theorem axc4i 2326

Description: Inference version of axc4 2325. (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 2152	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2214	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-10 2141  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-or 847  df-ex 1778  df-nf 1782

This theorem is referenced by:  hbae  2439  hbsb2  2490  hbsb2a  2492  hbsb2e  2494  nfabdwOLD  2933  reu6  3748  ralidm  4535  axunndlem1  10664  axacndlem3  10678  axacndlem5  10680  axacnd  10681  bj-nfs1t  36756  bj-hbs1  36778  bj-hbsb2av  36780  bj-hbaeb2  36784  wl-hbae1  37473  frege93  43918  spALT  44163  pm11.57  44358  pm11.59  44360  axc5c4c711toc7  44373  axc11next  44375  hbalg  44526  ax6e2eq  44528  ax6e2eqVD  44878  ichnfimlem  47337