Theorem moan 2017

Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)

Assertion

Ref	Expression
moan	|- ( E* x ph -> E* x ( ps /\ ph ) )

Proof of Theorem moan

Step	Hyp	Ref	Expression
1		simpr 108	. 2 |- ( ( ps /\ ph ) -> ph )
2	1	moimi 2013	1 |- ( E* x ph -> E* x ( ps /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 102   E*wmo 1949

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952

This theorem is referenced by:  moani  2018  mooran1  2020  mormo  2578  rmoan  2815