Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  elabgf0 Structured version   GIF version

Theorem elabgf0 9185
Description: Lemma for elabgf 2679. (Contributed by BJ, 21-Nov-2019.)
Assertion
Ref Expression
elabgf0 (x = A → (A {xφ} ↔ φ))

Proof of Theorem elabgf0
StepHypRef Expression
1 abid 2025 . 2 (x {xφ} ↔ φ)
2 eleq1 2097 . 2 (x = A → (x {xφ} ↔ A {xφ}))
31, 2syl5rbbr 184 1 (x = A → (A {xφ} ↔ φ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1242   wcel 1390  {cab 2023
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033
This theorem is referenced by:  elabgft1  9186  elabgf2  9188
  Copyright terms: Public domain W3C validator