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Theorem nfeu 2172
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 1544 . . 3  |-  F/ y  T.
2 nfeu.1 . . . 4  |-  F/ x ph
32a1i 10 . . 3  |-  (  T. 
->  F/ x ph )
41, 3nfeud 2170 . 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 1534   E!weu 2156
This theorem is referenced by:  2eu7  2242  2eu8  2243  eusv2nf  4548  reusv2lem3  4553  bnj1489  29402
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-eu 2160
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