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Theorem bnj1113 33064
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 4968 1 (𝐴 = 𝐵 𝑥𝐶 𝐸 = 𝑥𝐷 𝐸)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540   ciun 4941
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 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-rex 3071  df-v 3443  df-in 3905  df-ss 3915  df-iun 4943
This theorem is referenced by:  bnj106  33147  bnj222  33162  bnj540  33171  bnj553  33177  bnj611  33197  bnj966  33223  bnj1112  33262
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