Theorem moanimv 1431

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-17 973	. 2 |- (ph -> A.xph)
2	1	moanim 1429	1 |- (E*x(ph /\ ps) <-> (ph -> E*xps))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  E*wmo 1383

This theorem is referenced by:  2reuswap 1940  funcnv 3564  fncnv 3568  isarep2 3585  opabex 3616  zfrep6 3621  fnopabg 3622  fvopab3ig 3785  fnoprabg 4019  oprabex 4026  oprabvalig 4031  th3qcor 4323

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385

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