New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  spimeh Unicode version

Theorem spimeh 1667
 Description: Existential introduction, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. (Contributed by NM, 7-Aug-1994.) (Proof shortened by Wolf Lammen, 10-Dec-2017.)
Hypotheses
Ref Expression
spimeh.1
spimeh.2
Assertion
Ref Expression
spimeh
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem spimeh
StepHypRef Expression
1 spimeh.1 . 2
2 a9ev 1656 . . . 4
3 spimeh.2 . . . . 5
43eximi 1576 . . . 4
52, 4ax-mp 5 . . 3
6519.35i 1601 . 2
71, 6syl 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1540  wex 1541 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-9 1654 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by:  ax12olem1  1927  ax10lem2  1937
 Copyright terms: Public domain W3C validator