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Theorem moan 2095
Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
moan  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )

Proof of Theorem moan
StepHypRef Expression
1 simpr 110 . 2  |-  ( ( ps  /\  ph )  ->  ph )
21moimi 2091 1  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104   E*wmo 2027
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030
This theorem is referenced by:  moani  2096  mooran1  2098  mormo  2688  rmoan  2937
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