ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  spime Unicode version

Theorem spime 1671
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 1670 . 2  |-  ( T. 
->  ( ph  ->  E. x ps ) )
54trud 1294 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   T. wtru 1286   F/wnf 1390   E.wex 1422
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391
This theorem is referenced by:  spimev  1784
  Copyright terms: Public domain W3C validator