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  2430  hbsb2  2481  hbsb2a  2483  hbsb2e  2485  reu6  3700  ralidm  4478  axunndlem1  10555  axacndlem3  10569  axacndlem5  10571  axacnd  10572  bj-nfs1t  36785  bj-hbs1  36807  bj-hbsb2av  36809  bj-hbaeb2  36813  wl-hbae1  37514  frege93  43952  spALT  44197  pm11.57  44385  pm11.59  44387  axc5c4c711toc7  44400  axc11next  44402  hbalg  44552  ax6e2eq  44554  ax6e2eqVD  44903  ichnfimlem  47468