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Theorem bnj1424 32118
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 32068 . 2 (𝐷𝐴 ↔ (𝐷𝐵𝐷𝐶))
32biimpi 218 1 (𝐷𝐴 → (𝐷𝐵𝐷𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 843   = wceq 1537  wcel 2114  cun 3911
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2792
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ex 1781  df-sb 2070  df-clab 2799  df-cleq 2813  df-clel 2891  df-v 3475  df-un 3918
This theorem is referenced by:  bnj1423  32331  bnj1452  32332
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