Theorem elab1 16379

Description: One implication of elab 2950. (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 1576	. 2 |- F/ x ps
2		elab1.1	. 2 |- ( x = A -> ( ph -> ps ) )
3	1, 2	elabf1 16377	1 |- ( A e. { x | ph } -> ps )

Syntax hints:   -> wi 4   = wceq 1397   e. wcel 2202   {cab 2217

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804

This theorem is referenced by: (None)