Theorem axc4i 2321

Description: Inference version of axc4 2320. (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 2152	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2214	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-10 2142  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-or 848  df-ex 1780  df-nf 1784

This theorem is referenced by:  hbae  2429  hbsb2  2480  hbsb2a  2482  hbsb2e  2484  reu6  3697  ralidm  4475  axunndlem1  10548  axacndlem3  10562  axacndlem5  10564  axacnd  10565  bj-nfs1t  36778  bj-hbs1  36800  bj-hbsb2av  36802  bj-hbaeb2  36806  wl-hbae1  37507  frege93  43945  spALT  44190  pm11.57  44378  pm11.59  44380  axc5c4c711toc7  44393  axc11next  44395  hbalg  44545  ax6e2eq  44547  ax6e2eqVD  44896  ichnfimlem  47464