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Theorem moani 2195
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 2194 . 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 2144
This theorem is referenced by:  euxfr2  2950  reuxfr2d  4557  fvopab6  5621  1stconst  6207  2ndconst  6208  iunmapdisj  7650  axaddf  8767  axmulf  8768  reuxfr3d  23138  cmp2morp  25958  cmpmorfun  25971
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-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148
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