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Theorem moani 2076
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 2075 . 2  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )
31, 2ax-mp 5 1  |-  E* x
( ps  /\  ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 103   E*wmo 2007
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010
This theorem is referenced by:  euxfr2dc  2897  fvopab6  5566  1stconst  6170  2ndconst  6171  axaddf  7790  axmulf  7791
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