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Theorem moani 2019
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 2018 . 2  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )
31, 2ax-mp 7 1  |-  E* x
( ps  /\  ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 103   E*wmo 1950
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-eu 1952  df-mo 1953
This theorem is referenced by:  euxfr2dc  2801  fvopab6  5410  1stconst  6000  2ndconst  6001
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