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Theorem bnj1292 31203
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 4023 . 2 (𝐵𝐶) ⊆ 𝐵
31, 2eqsstri 3826 1 𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1637  cin 3762  wss 3763
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2067  ax-7 2103  ax-9 2164  ax-10 2184  ax-11 2200  ax-12 2213  ax-13 2419  ax-ext 2781
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2060  df-clab 2789  df-cleq 2795  df-clel 2798  df-nfc 2933  df-v 3389  df-in 3770  df-ss 3777
This theorem is referenced by:  bnj1253  31402  bnj1286  31404  bnj1280  31405  bnj1296  31406
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