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 ) )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105   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:  mosubt  3003  2reuswapdc  3030  2rmorex  3032  mosubopt  4835  funmo  5387  funcnv  5437  fncnv  5442  isarep2  5463  fnres  5495  fnopabg  5502  fvopab3ig  5773  opabex  5932  fnoprabg  6179  ovidi  6197  ovig  6200  oprabexd  6350  oprabex  6351  th3qcor  6903  dvfgg  15712