Theorem axc4i 2306

Description: Inference version of axc4 2305. (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 2123	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2180	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1523

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1781  ax-4 1795  ax-5 1892  ax-6 1951  ax-7 1996  ax-10 2114  ax-12 2143

This theorem depends on definitions:  df-bi 208  df-or 843  df-ex 1766  df-nf 1770

This theorem is referenced by:  hbae  2412  hbsb2  2477  hbsb2a  2479  hbsb2e  2481  hbsb2ALT  2555  reu6  3656  axunndlem1  9870  axacndlem3  9884  axacndlem5  9886  axacnd  9887  bj-nfs1t  33662  bj-hbs1  33690  bj-hbsb2av  33692  bj-hbaeb2  33717  wl-hbae1  34313  frege93  39808  spALT  40061  pm11.57  40280  pm11.59  40282  axc5c4c711toc7  40295  axc11next  40297  hbalg  40449  ax6e2eq  40451  ax6e2eqVD  40801