Theorem axc4i 2274

Description: Inference version of axc4 2273. (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 2173	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2225	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1626

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1867  ax-4 1882  ax-5 1984  ax-6 2050  ax-7 2086  ax-10 2164  ax-12 2192

This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1850  df-nf 1855

This theorem is referenced by:  hbae  2453  hbsb2  2492  hbsb2a  2494  hbsb2e  2496  reu6  3532  axunndlem1  9605  axacndlem3  9619  axacndlem5  9621  axacnd  9622  bj-nfs1t  33016  bj-hbs1  33060  bj-hbsb2av  33062  bj-hbaeb2  33107  wl-hbae1  33612  frege93  38748  pm11.57  39087  pm11.59  39089  axc5c4c711toc7  39103  axc11next  39105  hbalg  39269  ax6e2eq  39271  ax6e2eqVD  39638