Theorem moani 2157

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 2156	. 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 2087

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-eu 2089  df-mo 2090

This theorem is referenced by:  euxfr2dc  3011  fvopab6  5796  1stconst  6447  2ndconst  6448  axaddf  8225  axmulf  8226