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 31155
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 4689 1 (𝐴 = 𝐵 𝑥𝐶 𝐸 = 𝑥𝐷 𝐸)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1624   ciun 4664
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878  ax-5 1980  ax-6 2046  ax-7 2082  ax-9 2140  ax-10 2160  ax-11 2175  ax-12 2188  ax-13 2383  ax-ext 2732
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1627  df-ex 1846  df-nf 1851  df-sb 2039  df-clab 2739  df-cleq 2745  df-clel 2748  df-nfc 2883  df-ral 3047  df-rex 3048  df-v 3334  df-in 3714  df-ss 3721  df-iun 4666
This theorem is referenced by:  bnj106  31237  bnj222  31252  bnj540  31261  bnj553  31267  bnj611  31287  bnj966  31313  bnj1112  31350
  Copyright terms: Public domain W3C validator