MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  alim Structured version   Visualization version   GIF version

Theorem alim 1735
Description: Restatement of Axiom ax-4 1734, for labeling consistency. It should be the only theorem using ax-4 1734. (Contributed by NM, 10-Jan-1993.)
Assertion
Ref Expression
alim (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))

Proof of Theorem alim
StepHypRef Expression
1 ax-4 1734 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478
This theorem was proved from axioms:  ax-4 1734
This theorem is referenced by:  alimi  1736  al2im  1739  sylgt  1746  19.38a  1764  stdpc5v  1864  spfwOLD  1963  19.21tOLDOLD  2072  axc4  2126  19.21t-1OLD  2211  eunex  4824  hbaltg  31449  bj-2alim  32271  bj-alexim  32282  bj-hbalt  32348  bj-nfdt0  32362  bj-eunex  32477  stdpc5t  32492  al3im  37454  hbalg  38288  al2imVD  38616  hbalgVD  38659
  Copyright terms: Public domain W3C validator