Theorem mo4 1396

Description: "At most one" expressed using implicit substitution.

Hypothesis

Ref	Expression
mo4.1	|- (x = y -> (ph <-> ps))

Assertion

Ref	Expression
mo4	|- (E*xph <-> A.xA.y((ph /\ ps) -> x = y))

Distinct variable groups:   x,y   ph,y   ps,x

Proof of Theorem mo4

Step	Hyp	Ref	Expression
1		ax-17 968	. 2 |- (ps -> A.xps)
2		mo4.1	. 2 |- (x = y -> (ph <-> ps))
3	1, 2	mo4f 1395	1 |- (E*xph <-> A.xA.y((ph /\ ps) -> x = y))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  A.wal 951   = wceq 953  E*wmo 1374

This theorem is referenced by:  eu4 1403  rmo4 1923  dffun3 3513  fun11 3548  f1fv 3859  caoprmo 4056  th3qlem1 4298  supmo 4550  ajmoi 8450  spwmo 8580  adjmo 9675  bra11 9954

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376

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