Theorem elab1 11112

Description: One implication of elab 2751. (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 1464	. 2 |- F/ x ps
2		elab1.1	. 2 |- ( x = A -> ( ph -> ps ) )
3	1, 2	elabf1 11110	1 |- ( A e. { x | ph } -> ps )

Syntax hints:   -> wi 4   = wceq 1287   e. wcel 1436   {cab 2071

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 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067

This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617

This theorem is referenced by: (None)