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Theorem bnj1113 30110
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1113.1 (𝐴 = 𝐵𝐶 = 𝐷)
Assertion
Ref Expression
bnj1113 (𝐴 = 𝐵 𝑥𝐶 𝐸 = 𝑥𝐷 𝐸)
Distinct variable groups:   𝑥,𝐶   𝑥,𝐷
Allowed substitution hints:   𝐴(𝑥)   𝐵(𝑥)   𝐸(𝑥)

Proof of Theorem bnj1113
StepHypRef Expression
1 bnj1113.1 . 2 (𝐴 = 𝐵𝐶 = 𝐷)
21iuneq1d 4481 1 (𝐴 = 𝐵 𝑥𝐶 𝐸 = 𝑥𝐷 𝐸)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475  ∪ ciun 4455 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-v 3175  df-in 3547  df-ss 3554  df-iun 4457 This theorem is referenced by:  bnj106  30192  bnj222  30207  bnj540  30216  bnj553  30222  bnj611  30242  bnj966  30268  bnj1112  30305
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