Theorem elab2a 13819

Description: One implication of elab 2874. (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 1521	. 2 |- F/ x ps
2		elab2a.s	. 2 |- A e. _V
3		elab2a.1	. 2 |- ( x = A -> ( ps -> ph ) )
4	1, 2, 3	elabf2 13817	1 |- ( ps -> A e. { x | ph } )

Syntax hints:   -> wi 4   = wceq 1348   e. wcel 2141   {cab 2156   _Vcvv 2730

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732

This theorem is referenced by: (None)