MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.35i Structured version   Visualization version   GIF version

Theorem 19.35i 1977
Description: Inference associated with 19.35 1976. (Contributed by NM, 21-Jun-1993.)
Hypothesis
Ref Expression
19.35i.1 𝑥(𝜑𝜓)
Assertion
Ref Expression
19.35i (∀𝑥𝜑 → ∃𝑥𝜓)

Proof of Theorem 19.35i
StepHypRef Expression
1 19.35i.1 . 2 𝑥(𝜑𝜓)
2 19.35 1976 . 2 (∃𝑥(𝜑𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
31, 2mpbi 221 1 (∀𝑥𝜑 → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1650  wex 1874
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904
This theorem depends on definitions:  df-bi 198  df-ex 1875
This theorem is referenced by:  19.2  2074  spimeh  2095  ax6e  2356  spimed  2361  equvini  2436  equvel  2437  euexOLD  2619  axrep4  4935  zfcndrep  9689  bj-ax6elem2  33088  bj-spimedv  33154  bj-axrep4  33221  wl-exeq  33746  spd  43094
  Copyright terms: Public domain W3C validator