Theorem moanimv 2156

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 1577	. 2 |- F/ x ph
2	1	moanim 2155	1 |- ( E* x ( ph /\ ps ) <-> ( ph -> E* x ps ) )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105   E*wmo 2081

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-eu 2083  df-mo 2084

This theorem is referenced by:  mosubt  2994  2reuswapdc  3021  2rmorex  3023  mosubopt  4815  funmo  5367  funcnv  5417  fncnv  5422  isarep2  5443  fnres  5475  fnopabg  5482  fvopab3ig  5751  opabex  5910  fnoprabg  6154  ovidi  6172  ovig  6175  oprabexd  6320  oprabex  6321  th3qcor  6873  dvfgg  15553