Theorem axc4i 2325

Description: Inference version of axc4 2324. (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 2156	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2218	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 2146  ax-12 2182

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

This theorem is referenced by:  hbae  2433  hbsb2  2484  hbsb2a  2486  hbsb2e  2488  reu6  3681  ralidm  4461  axunndlem1  10493  axacndlem3  10507  axacndlem5  10509  axacnd  10510  bj-nfs1t  36855  bj-hbs1  36877  bj-hbsb2av  36879  bj-hbaeb2  36883  wl-hbae1  37584  frege93  44074  spALT  44319  pm11.57  44507  pm11.59  44509  axc5c4c711toc7  44522  axc11next  44524  hbalg  44673  ax6e2eq  44675  ax6e2eqVD  45024  ichnfimlem  47588