ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.37aiv GIF version

Theorem 19.37aiv 1565
Description: Inference from Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.37aiv.1 𝑥(𝜑𝜓)
Assertion
Ref Expression
19.37aiv (𝜑 → ∃𝑥𝜓)
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem 19.37aiv
StepHypRef Expression
1 19.37aiv.1 . 2 𝑥(𝜑𝜓)
2 nfv 1421 . . 3 𝑥𝜑
3219.37-1 1564 . 2 (∃𝑥(𝜑𝜓) → (𝜑 → ∃𝑥𝜓))
41, 3ax-mp 7 1 (𝜑 → ∃𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by:  eqvinc  2667  limom  4336
  Copyright terms: Public domain W3C validator