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Theorem bnj1424 32554
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1424.1 𝐴 = (𝐵𝐶)
Assertion
Ref Expression
bnj1424 (𝐷𝐴 → (𝐷𝐵𝐷𝐶))

Proof of Theorem bnj1424
StepHypRef Expression
1 bnj1424.1 . . 3 𝐴 = (𝐵𝐶)
21bnj1138 32504 . 2 (𝐷𝐴 ↔ (𝐷𝐵𝐷𝐶))
32biimpi 219 1 (𝐷𝐴 → (𝐷𝐵𝐷𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 847   = wceq 1543  wcel 2111  cun 3879
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2113  ax-9 2121  ax-ext 2709
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-ex 1788  df-sb 2072  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3423  df-un 3886
This theorem is referenced by:  bnj1423  32767  bnj1452  32768
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