Theorem elab2a 14621

Description: One implication of elab 2883. (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 1528	. 2 |- F/ x ps
2		elab2a.s	. 2 |- A e. _V
3		elab2a.1	. 2 |- ( x = A -> ( ps -> ph ) )
4	1, 2, 3	elabf2 14619	1 |- ( ps -> A e. { x | ph } )

Syntax hints:   -> wi 4   = wceq 1353   e. wcel 2148   {cab 2163   _Vcvv 2739

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741

This theorem is referenced by: (None)