ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.25 GIF version

Theorem 19.25 1533
Description: Theorem 19.25 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)
Assertion
Ref Expression
19.25 (∀𝑦𝑥(𝜑𝜓) → (∃𝑦𝑥𝜑 → ∃𝑦𝑥𝜓))

Proof of Theorem 19.25
StepHypRef Expression
1 19.35-1 1531 . . 3 (∃𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∃𝑥𝜓))
21alimi 1360 . 2 (∀𝑦𝑥(𝜑𝜓) → ∀𝑦(∀𝑥𝜑 → ∃𝑥𝜓))
3 exim 1506 . 2 (∀𝑦(∀𝑥𝜑 → ∃𝑥𝜓) → (∃𝑦𝑥𝜑 → ∃𝑦𝑥𝜓))
42, 3syl 14 1 (∀𝑦𝑥(𝜑𝜓) → (∃𝑦𝑥𝜑 → ∃𝑦𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1257  wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator