Theorem moanimv 2074

Description: Introduction of a conjunct into at-most-one quantifier. (Contributed by NM, 23-Mar-1995.)

Assertion

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

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem moanimv

Step	Hyp	Ref	Expression
1		nfv 1508	. 2 |- F/ x ph
2	1	moanim 2073	1 |- ( E* x ( ph /\ ps ) <-> ( ph -> E* x ps ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104   E*wmo 2000

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003

This theorem is referenced by:  mosubt  2861  2reuswapdc  2888  2rmorex  2890  mosubopt  4604  funmo  5138  funcnv  5184  fncnv  5189  isarep2  5210  fnres  5239  fnopabg  5246  fvopab3ig  5495  opabex  5644  fnoprabg  5872  ovidi  5889  ovig  5892  oprabexd  6025  oprabex  6026  th3qcor  6533  dvfgg  12826