Theorem moanimv 2101

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 1528	. 2 |- F/ x ph
2	1	moanim 2100	1 |- ( E* x ( ph /\ ps ) <-> ( ph -> E* x ps ) )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105   E*wmo 2027

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030

This theorem is referenced by:  mosubt  2914  2reuswapdc  2941  2rmorex  2943  mosubopt  4690  funmo  5230  funcnv  5276  fncnv  5281  isarep2  5302  fnres  5331  fnopabg  5338  fvopab3ig  5589  opabex  5739  fnoprabg  5973  ovidi  5990  ovig  5993  oprabexd  6125  oprabex  6126  th3qcor  6636  dvfgg  14028