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Theorem moani 2208
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 2207 . 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 358   E*wmo 2157
This theorem is referenced by:  euxfr2  2963  reuxfr2d  4573  fvopab6  5637  1stconst  6223  2ndconst  6224  iunmapdisj  7666  axaddf  8783  axmulf  8784  reuxfr3d  23154  cmp2morp  26061  cmpmorfun  26074
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-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161
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