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Theorem spime 1960
 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 1958 . 2
54trud 1329 1
 Colors of variables: wff set class Syntax hints:   wi 4   wtru 1322  wex 1547  wnf 1550 This theorem is referenced by:  spimev  1962  exnel  25373 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757  ax-12 1946 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551
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