Theorem moanimv 2162

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 1581	. 2 |- F/ x ph
2	1	moanim 2161	1 |- ( E* x ( ph /\ ps ) <-> ( ph -> E* x ps ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   <-> wb 105   E*wmo 2087

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

This theorem is used by:  mosubt  3003  2reuswapdc  3030  2rmorex  3032  mosubopt  4842  funmo  5395  funcnv  5445  fncnv  5450  isarep2  5471  fnres  5503  fnopabg  5510  fvopab3ig  5782  opabex  5944  fnoprabg  6192  ovidi  6210  ovig  6213  oprabexd  6364  oprabex  6365  th3qcor  6917  dvfgg  15914