Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  a4ime Unicode version

Theorem a4ime 1869
 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.)
Hypotheses
Ref Expression
a4ime.1
a4ime.2
Assertion
Ref Expression
a4ime

Proof of Theorem a4ime
StepHypRef Expression
1 a4ime.1 . . . . 5
21nfn 1731 . . . 4
3 a4ime.2 . . . . 5
43con3d 127 . . . 4
52, 4a4im 1868 . . 3
65con2i 114 . 2
7 df-ex 1538 . 2
86, 7sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6  wal 1532  wex 1537  wnf 1539   wceq 1619 This theorem is referenced by:  a4imed  1870  a4imev  1998  exnel  23493 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-9 1684  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540
 Copyright terms: Public domain W3C validator