Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1113 Structured version   Visualization version   GIF version

Theorem bnj1113 34641
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 5021 1 (𝐴 = 𝐵 𝑥𝐶 𝐸 = 𝑥𝐷 𝐸)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1534   ciun 4994
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-rex 3061  df-v 3465  df-ss 3964  df-iun 4996
This theorem is referenced by:  bnj106  34724  bnj222  34739  bnj540  34748  bnj553  34754  bnj611  34774  bnj966  34800  bnj1112  34839
  Copyright terms: Public domain W3C validator