Theorem cla4v 1868

Description: Rule of specialization with implicit substitution.

Hypotheses

Ref	Expression
cla4v.1	|- A e. V
cla4v.2	|- (x = A -> (ph <-> ps))

Assertion

Ref	Expression
cla4v	|- (A.xph -> ps)

Distinct variable groups:   x,A   ps,x

Proof of Theorem cla4v

Step	Hyp	Ref	Expression
1		cla4v.1	. 2 |- A e. V
2		cla4v.2	. . 3 |- (x = A -> (ph <-> ps))
3	2	cla4gv 1862	. 2 |- (A e. V -> (A.xph -> ps))
4	1, 3	ax-mp 7	1 |- (A.xph -> ps)

Syntax hints:   -> wi 3   <-> wb 146  A.wal 954   = wceq 956   e. wcel 958  Vcvv 1811

This theorem is referenced by:  csbiegft 2029  rext 2754  frc 2920  relop 3275  pw2en 4446  pssnn 4534  unifiOLD 4557  fiint 4559  fiintOLD 4560  fodomfiOLD 4566  dfom3 4630  elom3 4631  aceq3lem 4732  aceq3 4733  aceq5lem4 4738  kmlem1 4765  kmlem4 4768  kmlem10 4774  zorn2lem7 4794  prlem934a 5137  suppsrlem 5221  nnunb 6070  dfuz 6202  chlim 9104

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-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812

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