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Theorem spimeh 1679
 Description: Existential introduction, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. (Contributed by NM, 7-Aug-1994.) (Proof shortened by Wolf Lammen, 10-Dec-2017.)
Hypotheses
Ref Expression
spimeh.1
spimeh.2
Assertion
Ref Expression
spimeh
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem spimeh
StepHypRef Expression
1 spimeh.1 . 2
2 a9ev 1668 . . . 4
3 spimeh.2 . . . 4
42, 3eximii 1587 . . 3
5419.35i 1611 . 2
61, 5syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549  wex 1550 This theorem is referenced by:  ax12olem1OLD  2011  ax10lem2OLD  2026 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-9 1666 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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