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Theorem 19.35i 1803
Description: Inference associated with 19.35 1802. (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 1802 . 2 (∃𝑥(𝜑𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
31, 2mpbi 220 1 (∀𝑥𝜑 → ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  wex 1701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by:  19.2  1889  spimeh  1922  cbv3hvOLD  2172  cbv3hvOLDOLD  2173  ax6e  2249  spimed  2254  equvini  2345  equvel  2346  euex  2493  axrep4  4745  zfcndrep  9396  bj-ax6elem2  32347  bj-spimedv  32414  bj-axrep4  32487  wl-exeq  32992  spd  41747
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