Theorem moani 2070

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

Step	Hyp	Ref	Expression
1		moani.1	. 2 |- E* x ph
2		moan 2069	. 2 |- ( E* x ph -> E* x ( ps /\ ph ) )
3	1, 2	ax-mp 5	1 |- E* x ( ps /\ ph )

Syntax hints:   /\ wa 103   E*wmo 2001

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004

This theorem is referenced by:  euxfr2dc  2873  fvopab6  5525  1stconst  6126  2ndconst  6127  axaddf  7700  axmulf  7701