Theorem moanimv 2023

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 1466	. 2 |- F/ x ph
2	1	moanim 2022	1 |- ( E* x ( ph /\ ps ) <-> ( ph -> E* x ps ) )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103   E*wmo 1949

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952

This theorem is referenced by:  mosubt  2792  2reuswapdc  2819  2rmorex  2821  mosubopt  4503  funmo  5030  funcnv  5075  fncnv  5080  isarep2  5101  fnres  5130  fnopabg  5137  fvopab3ig  5378  opabex  5521  fnoprabg  5746  ovidi  5763  ovig  5766  oprabexd  5898  oprabex  5899  th3qcor  6394