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Theorem spime 1719
 Description: Existential introduction, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 6-Mar-2018.)
Hypotheses
Ref Expression
spime.1
spime.2
Assertion
Ref Expression
spime

Proof of Theorem spime
StepHypRef Expression
1 spime.1 . . . 4
21a1i 9 . . 3
3 spime.2 . . 3
42, 3spimed 1718 . 2
54mptru 1340 1
 Colors of variables: wff set class Syntax hints:   wi 4   wtru 1332  wnf 1436  wex 1468 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-i9 1510  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437 This theorem is referenced by:  spimev  1833
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