Theorem elabgf0 11020

Description: Lemma for elabgf 2746. (Contributed by BJ, 21-Nov-2019.)

Assertion

Ref	Expression
elabgf0	|- ( x = A -> ( A e. { x | ph } <-> ph ) )

Proof of Theorem elabgf0

Step	Hyp	Ref	Expression
1		abid 2071	. 2 |- ( x e. { x | ph } <-> ph )
2		eleq1 2145	. 2 |- ( x = A -> ( x e. { x | ph } <-> A e. { x | ph } ) )
3	1, 2	syl5rbbr 193	1 |- ( x = A -> ( A e. { x | ph } <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 103   = wceq 1285   e. wcel 1434   {cab 2069

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-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079

This theorem is referenced by:  elabgft1  11021  elabgf2  11023