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

Theorem spime 1602
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/
spime.2
Assertion
Ref Expression
spime

Proof of Theorem spime
StepHypRef Expression
1 spime.1 . . . 4  F/
21a1i 9 . . 3  F/
3 spime.2 . . 3
42, 3spimed 1601 . 2
54trud 1232 1
Colors of variables: wff set class
Syntax hints:   wi 4   wtru 1224   F/wnf 1322  wex 1354
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1309  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-4 1373  ax-i9 1396  ax-ial 1400
This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323
This theorem is referenced by:  spimev  1714
  Copyright terms: Public domain W3C validator