Theorem moani 2124

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 2123	. 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 2055

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-eu 2057  df-mo 2058

This theorem is referenced by:  euxfr2dc  2958  fvopab6  5676  1stconst  6307  2ndconst  6308  axaddf  7981  axmulf  7982