Theorem moanimv 2117

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 1539	. 2 |- F/ x ph
2	1	moanim 2116	1 |- ( E* x ( ph /\ ps ) <-> ( ph -> E* x ps ) )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105   E*wmo 2043

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-eu 2045  df-mo 2046

This theorem is referenced by:  mosubt  2938  2reuswapdc  2965  2rmorex  2967  mosubopt  4725  funmo  5270  funcnv  5316  fncnv  5321  isarep2  5342  fnres  5371  fnopabg  5378  fvopab3ig  5632  opabex  5783  fnoprabg  6020  ovidi  6038  ovig  6041  oprabexd  6181  oprabex  6182  th3qcor  6695  dvfgg  14867