Theorem rsp 2674

Description: Restricted specialization. (Contributed by NM, 17-Oct-1996.)

Assertion

Ref	Expression
rsp	|- (A.x e. A ph -> (x e. A -> ph))

Proof of Theorem rsp

Step	Hyp	Ref	Expression
1		df-ral 2619	. 2 |- (A.x e. A ph <-> A.x(x e. A -> ph))
2		sp 1747	. 2 |- (A.x(x e. A -> ph) -> (x e. A -> ph))
3	1, 2	sylbi 187	1 |- (A.x e. A ph -> (x e. A -> ph))

Syntax hints:   -> wi 4  A.wal 1540   e. wcel 1710  A.wral 2614

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-ral 2619

This theorem is referenced by:  rsp2  2676  rspec  2678  r19.12  2727  ralbi  2750  reupick2  3541  dfiun2g  3999  iinss2  4018  pw1disj  4167  sfinltfin  4535  fun11iun  5305  chfnrn  5399  ffnfv  5427  mpteq12f  5655  mpt2eq123  5661  fvmptss  5705