Theorem elab2a 16106

Description: One implication of elab 2947. (Contributed by BJ, 21-Nov-2019.)

Hypotheses

Ref	Expression
elab2a.s	|- A e. _V
elab2a.1	|- ( x = A -> ( ps -> ph ) )

Assertion

Ref	Expression
elab2a	|- ( ps -> A e. { x | ph } )

Distinct variable groups:   ps, x   x, A

Allowed substitution hint:   ph( x)

Proof of Theorem elab2a

Step	Hyp	Ref	Expression
1		nfv 1574	. 2 |- F/ x ps
2		elab2a.s	. 2 |- A e. _V
3		elab2a.1	. 2 |- ( x = A -> ( ps -> ph ) )
4	1, 2, 3	elabf2 16104	1 |- ( ps -> A e. { x | ph } )

Syntax hints:   -> wi 4   = wceq 1395   e. wcel 2200   {cab 2215   _Vcvv 2799

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801

This theorem is referenced by: (None)