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

Theorem nfeu 2159
Description: Bound-variable hypothesis builder for "at most one." Note that  x and  y needn't be distinct (this makes the proof more difficult). (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.)
Hypothesis
Ref Expression
nfeu.1  |-  F/ x ph
Assertion
Ref Expression
nfeu  |-  F/ x E! y ph

Proof of Theorem nfeu
StepHypRef Expression
1 nftru 1541 . . 3  |-  F/ y  T.
2 nfeu.1 . . . 4  |-  F/ x ph
32a1i 10 . . 3  |-  (  T. 
->  F/ x ph )
41, 3nfeud 2157 . 2  |-  (  T. 
->  F/ x E! y
ph )
54trud 1314 1  |-  F/ x E! y ph
Colors of variables: wff set class
Syntax hints:    T. wtru 1307   F/wnf 1531   E!weu 2143
This theorem is referenced by:  2eu7  2229  2eu8  2230  eusv2nf  4532  reusv2lem3  4537  bnj1489  29086
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-eu 2147
  Copyright terms: Public domain W3C validator