Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1424 Structured version   Visualization version   GIF version

Theorem bnj1424 31247
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1424.1 𝐴 = (𝐵𝐶)
Assertion
Ref Expression
bnj1424 (𝐷𝐴 → (𝐷𝐵𝐷𝐶))

Proof of Theorem bnj1424
StepHypRef Expression
1 bnj1424.1 . . 3 𝐴 = (𝐵𝐶)
21bnj1138 31197 . 2 (𝐷𝐴 ↔ (𝐷𝐵𝐷𝐶))
32biimpi 206 1 (𝐷𝐴 → (𝐷𝐵𝐷𝐶))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 836   = wceq 1631   ∈ wcel 2145   ∪ cun 3721 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-v 3353  df-un 3728 This theorem is referenced by:  bnj1423  31457  bnj1452  31458
 Copyright terms: Public domain W3C validator