Theorem mo4 1402

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-17 970	. 2 |- (ps -> A.xps)
2		mo4.1	. 2 |- (x = y -> (ph <-> ps))
3	1, 2	mo4f 1401	1 |- (E*xph <-> A.xA.y((ph /\ ps) -> x = y))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  A.wal 953   = wceq 955  E*wmo 1380

This theorem is referenced by:  eu4 1409  rmo4 1930  dffun3 3523  fun11 3558  f1fv 3869  caoprmo 4065  th3qlem1 4307  supmo 4559  ajmoi 8478  spwmo 8613  adjmo 9715  bra11 9997

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-11 966  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1171  df-eu 1381  df-mo 1382

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