Theorem moanimv 1429

Description: Introduction of a conjunct into "at most one" quantifier.

Assertion

Ref	Expression
moanimv	|- (E*x(ph /\ ps) <-> (ph -> E*xps))

Distinct variable group:   ph,x

Proof of Theorem moanimv

Step	Hyp	Ref	Expression
1		ax-17 971	. 2 |- (ph -> A.xph)
2	1	moanim 1427	1 |- (E*x(ph /\ ps) <-> (ph -> E*xps))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  E*wmo 1381

This theorem is referenced by:  2reuswap 1937  funcnv 3557  fncnv 3561  isarep2 3578  opabex 3609  zfrep6 3614  fnopabg 3615  fvopab3ig 3778  fnoprabg 4012  oprabex 4019  oprabvalig 4024  th3qcor 4316

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383

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