Theorem axc4i 2131

Description: Inference version of axc4 2130. (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 2028	. 2 ⊢ Ⅎ𝑥∀𝑥𝜑
2		axc4i.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimi 2082	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by:  hbae  2315  hbsb2  2359  hbsb2a  2361  hbsb2e  2363  reu6  3395  axunndlem1  9417  axacndlem3  9431  axacndlem5  9433  axacnd  9434  bj-nfs1t  32714  bj-hbs1  32758  bj-hbsb2av  32760  bj-hbaeb2  32805  wl-hbae1  33303  frege93  38250  pm11.57  38589  pm11.59  38591  axc5c4c711toc7  38605  axc11next  38607  hbalg  38771  ax6e2eq  38773  ax6e2eqVD  39143