Theorem moani 2126

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 2125	. 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 2056

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-eu 2058  df-mo 2059

This theorem is referenced by:  euxfr2dc  2965  fvopab6  5699  1stconst  6330  2ndconst  6331  axaddf  8016  axmulf  8017