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 34807
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 4244 . 2 (𝐵𝐶) ⊆ 𝐵
31, 2eqsstri 4029 1 𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1536  cin 3961  wss 3962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3479  df-in 3969  df-ss 3979
This theorem is referenced by:  bnj1253  35009  bnj1286  35011  bnj1280  35012  bnj1296  35013
  Copyright terms: Public domain W3C validator