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Theorem bnj1113 32131
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 4921 1 (𝐴 = 𝐵 𝑥𝐶 𝐸 = 𝑥𝐷 𝐸)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538   ciun 4894
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-ral 3135  df-rex 3136  df-v 3471  df-in 3915  df-ss 3925  df-iun 4896
This theorem is referenced by:  bnj106  32214  bnj222  32229  bnj540  32238  bnj553  32244  bnj611  32264  bnj966  32290  bnj1112  32329
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