Theorem axc4i 2341

Description: Inference version of axc4 2340. (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 2155	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2213	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 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-12 2177

This theorem depends on definitions:  df-bi 209  df-or 844  df-ex 1781  df-nf 1785

This theorem is referenced by:  hbae  2453  hbsb2  2521  hbsb2a  2523  hbsb2e  2525  hbsb2ALT  2599  nfabdw  3002  reu6  3719  axunndlem1  10019  axacndlem3  10033  axacndlem5  10035  axacnd  10036  bj-nfs1t  34114  bj-hbs1  34136  bj-hbsb2av  34138  bj-hbaeb2  34143  wl-hbae1  34761  frege93  40309  spALT  40561  pm11.57  40728  pm11.59  40730  axc5c4c711toc7  40743  axc11next  40745  hbalg  40896  ax6e2eq  40898  ax6e2eqVD  41248