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

Theorem nfmo 2271
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
nfeu.1  |-  F/ x ph
Assertion
Ref Expression
nfmo  |-  F/ x E* y ph

Proof of Theorem nfmo
StepHypRef Expression
1 nftru 1560 . . 3  |-  F/ y  T.
2 nfeu.1 . . . 4  |-  F/ x ph
32a1i 11 . . 3  |-  (  T. 
->  F/ x ph )
41, 3nfmod 2269 . 2  |-  (  T. 
->  F/ x E* y ph )
54trud 1329 1  |-  F/ x E* y ph
Colors of variables: wff set class
Syntax hints:    T. wtru 1322   F/wnf 1550   E*wmo 2255
This theorem is referenced by:  moexex  2323  2moex  2325  2euex  2326  mosubopt  4414  reusv1  4682  reusv2lem1  4683  dffun6f  5427
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-eu 2258  df-mo 2259
  Copyright terms: Public domain W3C validator