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Theorem spime 2008
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 11 . . 3
3 spime.2 . . 3
42, 3spimed 2007 . 2
54trud 1404 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4   wtru 1396  E.wex 1612  F/wnf 1616
This theorem is referenced by:  spimev  2010  exnel  29235
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617
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