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Theorem spime 1962
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  |-  F/ x ph
spime.2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
spime  |-  ( ph  ->  E. x ps )

Proof of Theorem spime
StepHypRef Expression
1 spime.1 . . . 4  |-  F/ x ph
21a1i 11 . . 3  |-  (  T. 
->  F/ x ph )
3 spime.2 . . 3  |-  ( x  =  y  ->  ( ph  ->  ps ) )
42, 3spimed 1960 . 2  |-  (  T. 
->  ( ph  ->  E. x ps ) )
54trud 1332 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    T. wtru 1325   E.wex 1550   F/wnf 1553
This theorem is referenced by:  spimev  1964  exnel  25430
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-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554
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