Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  spime Unicode version

Theorem spime 1964
 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
spime.2
Assertion
Ref Expression
spime

Proof of Theorem spime
StepHypRef Expression
1 spime.1 . . . 4
21a1i 11 . . 3
3 spime.2 . . 3
42, 3spimed 1963 . 2
54trud 1379 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4   wtru 1371  E.wex 1587  F/wnf 1590 This theorem is referenced by:  spimev  1966  exnel  28072 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794  ax-13 1955 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591
 Copyright terms: Public domain W3C validator