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Theorem bnj1292 33094
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 4175 . 2 (𝐵𝐶) ⊆ 𝐵
31, 2eqsstri 3966 1 𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cin 3897  wss 3898
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3443  df-in 3905  df-ss 3915
This theorem is referenced by:  bnj1253  33296  bnj1286  33298  bnj1280  33299  bnj1296  33300
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