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Theorem spime 1676
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 9 . . 3  |-  ( T. 
->  F/ x ph )
3 spime.2 . . 3  |-  ( x  =  y  ->  ( ph  ->  ps ) )
42, 3spimed 1675 . 2  |-  ( T. 
->  ( ph  ->  E. x ps ) )
54mptru 1298 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   T. wtru 1290   F/wnf 1394   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-i9 1468  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395
This theorem is referenced by:  spimev  1789
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