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Theorem moani 2333
Description: "At most one" is still true when a conjunct is added. (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
moani.1  |-  E* x ph
Assertion
Ref Expression
moani  |-  E* x
( ps  /\  ph )

Proof of Theorem moani
StepHypRef Expression
1 moani.1 . 2  |-  E* x ph
2 moan 2332 . 2  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )
31, 2ax-mp 8 1  |-  E* x
( ps  /\  ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 359   E*wmo 2282
This theorem is referenced by:  euxfr2  3112  reuxfr2d  4739  fvopab6  5819  1stconst  6428  2ndconst  6429  iunmapdisj  7897  axaddf  9013  axmulf  9014  reuxfr3d  23969
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286
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