Theorem elab1 10593

Description: One implication of elab 2738. (Contributed by BJ, 21-Nov-2019.)

Hypothesis

Ref	Expression
elab1.1	|- ( x = A -> ( ph -> ps ) )

Assertion

Ref	Expression
elab1	|- ( A e. { x | ph } -> ps )

Distinct variable groups:   ps, x   x, A

Allowed substitution hint:   ph( x)

Proof of Theorem elab1

Step	Hyp	Ref	Expression
1		nfv 1461	. 2 |- F/ x ps
2		elab1.1	. 2 |- ( x = A -> ( ph -> ps ) )
3	1, 2	elabf1 10591	1 |- ( A e. { x | ph } -> ps )

Syntax hints:   -> wi 4   = wceq 1284   e. wcel 1433   {cab 2067

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603

This theorem is referenced by: (None)