Theorem moanimv 2094

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 1521	. 2 |- F/ x ph
2	1	moanim 2093	1 |- ( E* x ( ph /\ ps ) <-> ( ph -> E* x ps ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104   E*wmo 2020

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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-eu 2022  df-mo 2023

This theorem is referenced by:  mosubt  2907  2reuswapdc  2934  2rmorex  2936  mosubopt  4676  funmo  5213  funcnv  5259  fncnv  5264  isarep2  5285  fnres  5314  fnopabg  5321  fvopab3ig  5570  opabex  5720  fnoprabg  5954  ovidi  5971  ovig  5974  oprabexd  6106  oprabex  6107  th3qcor  6617  dvfgg  13451