Theorem axc4i 2323

Description: Inference version of axc4 2322. (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 2154	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2216	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1539

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-10 2144  ax-12 2180

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1781  df-nf 1785

This theorem is referenced by:  hbae  2431  hbsb2  2482  hbsb2a  2484  hbsb2e  2486  reu6  3685  ralidm  4462  axunndlem1  10486  axacndlem3  10500  axacndlem5  10502  axacnd  10503  bj-nfs1t  36830  bj-hbs1  36852  bj-hbsb2av  36854  bj-hbaeb2  36858  wl-hbae1  37559  frege93  43995  spALT  44240  pm11.57  44428  pm11.59  44430  axc5c4c711toc7  44443  axc11next  44445  hbalg  44594  ax6e2eq  44596  ax6e2eqVD  44945  ichnfimlem  47500