Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1292 Structured version   Visualization version   GIF version

Theorem bnj1292 34382
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1292.1 𝐴 = (𝐵𝐶)
Assertion
Ref Expression
bnj1292 𝐴𝐵

Proof of Theorem bnj1292
StepHypRef Expression
1 bnj1292.1 . 2 𝐴 = (𝐵𝐶)
2 inss1 4224 . 2 (𝐵𝐶) ⊆ 𝐵
31, 2eqsstri 4012 1 𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534  cin 3943  wss 3944
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 2698
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-v 3471  df-in 3951  df-ss 3961
This theorem is referenced by:  bnj1253  34584  bnj1286  34586  bnj1280  34587  bnj1296  34588
  Copyright terms: Public domain W3C validator