Theorem axc4i 2319

Description: Inference version of axc4 2318. (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 2151	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2209	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 1801  ax-4 1815  ax-5 1916  ax-6 1974  ax-7 2014  ax-10 2140  ax-12 2174

This theorem depends on definitions:  df-bi 206  df-or 844  df-ex 1786  df-nf 1790

This theorem is referenced by:  hbae  2432  hbsb2  2487  hbsb2a  2489  hbsb2e  2491  nfabdwOLD  2932  reu6  3664  ralidm  4447  axunndlem1  10335  axacndlem3  10349  axacndlem5  10351  axacnd  10352  bj-nfs1t  34951  bj-hbs1  34973  bj-hbsb2av  34975  bj-hbaeb2  34980  wl-hbae1  35657  frege93  41517  spALT  41765  pm11.57  41960  pm11.59  41962  axc5c4c711toc7  41975  axc11next  41977  hbalg  42128  ax6e2eq  42130  ax6e2eqVD  42480  ichnfimlem  44867