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Theorem elab1 7029
Description: One implication of elab 2664. (Contributed by BJ, 21-Nov-2019.)
Hypothesis
Ref Expression
elab1.1 (x = A → (φψ))
Assertion
Ref Expression
elab1 (A {xφ} → ψ)
Distinct variable groups:   ψ,x   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem elab1
StepHypRef Expression
1 nfv 1402 . 2 xψ
2 elab1.1 . 2 (x = A → (φψ))
31, 2elabf1 7027 1 (A {xφ} → ψ)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1228   wcel 1374  {cab 2008
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-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537
This theorem is referenced by: (None)
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