Theorem alim 1842

Description: Restatement of Axiom ax-4 1841, for labeling consistency. It should be the only theorem using ax-4 1841. (Contributed by NM, 10-Jan-1993.)

Assertion

Ref	Expression
alim	⊢ (∀𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))

Proof of Theorem alim

Step	Hyp	Ref	Expression
1		ax-4 1841	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-4 1841

This theorem is used by:  alimi  1843  al2im  1846  sylgt  1854  19.38a  1872  stdpc5v  1972  axc4  2354  hbaltg  36696  bj-almp  37608  bj-sylggt  37609  bj-2alim  37619  bj-exim  37636  bj-alexim  37637  bj-nfdt0  37724  bj-nnf-alrim  37774  bj-nnflemaa  37815  bj-nnflemea  37818  stdpc5t  37866  al3im  44787  hbalg  45677  al2imVD  45983  hbalgVD  46026