Theorem axc4i 2328

Description: Inference version of axc4 2327. (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 2157	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2221	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-10 2147  ax-12 2185

This theorem depends on definitions:  df-bi 207  df-or 849  df-ex 1782  df-nf 1786

This theorem is referenced by:  hbae  2436  hbsb2  2487  hbsb2a  2489  hbsb2e  2491  reu6  3686  ralidm  4472  axunndlem1  10518  axacndlem3  10532  axacndlem5  10534  axacnd  10535  bj-nfs1t  37035  bj-hbs1  37057  bj-hbsb2av  37059  bj-hbaeb2  37063  wl-hbae1  37771  frege93  44309  spALT  44554  pm11.57  44742  pm11.59  44744  axc5c4c711toc7  44757  axc11next  44759  hbalg  44908  ax6e2eq  44910  ax6e2eqVD  45259  ichnfimlem  47820