Theorem mo4 1403

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-17 971	. 2 |- (ps -> A.xps)
2		mo4.1	. 2 |- (x = y -> (ph <-> ps))
3	1, 2	mo4f 1402	1 |- (E*xph <-> A.xA.y((ph /\ ps) -> x = y))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  A.wal 954   = wceq 956  E*wmo 1381

This theorem is referenced by:  eu4 1410  rmo4 1933  dffun3 3527  fun11 3562  f1fv 3874  caoprmo 4070  th3qlem1 4314  supmo 4576  ajmoi 8519  spwmo 8656  adjmo 9758  bra11 10041

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

Copyright terms: Public domain