Theorem moani 2123

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 2122	. 2 |- ( E* x ph -> E* x ( ps /\ ph ) )
3	1, 2	ax-mp 5	1 |- E* x ( ps /\ ph )

Syntax hints:   /\ wa 104   E*wmo 2054

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 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-eu 2056  df-mo 2057

This theorem is referenced by:  euxfr2dc  2957  fvopab6  5675  1stconst  6306  2ndconst  6307  axaddf  7980  axmulf  7981