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

Theorem spimed 1961
 Description: Deduction version of spime 1963. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 19-Feb-2018.)
Hypotheses
Ref Expression
spimed.1
spimed.2
Assertion
Ref Expression
spimed

Proof of Theorem spimed
StepHypRef Expression
1 spimed.1 . . 3
21nfrd 1780 . 2
3 a9e 1953 . . . 4
4 spimed.2 . . . 4
53, 4eximii 1588 . . 3
6519.35i 1612 . 2
72, 6syl6 32 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1550  wex 1551  wnf 1554 This theorem is referenced by:  spime  1963  equvini  2084  equviniOLD  2085 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
 Copyright terms: Public domain W3C validator