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Theorem bnj1213 31201
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1213.1 𝐴𝐵
bnj1213.2 (𝜃𝑥𝐴)
Assertion
Ref Expression
bnj1213 (𝜃𝑥𝐵)

Proof of Theorem bnj1213
StepHypRef Expression
1 bnj1213.1 . 2 𝐴𝐵
2 bnj1213.2 . 2 (𝜃𝑥𝐴)
31, 2sseldi 3748 1 (𝜃𝑥𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2144  wss 3721
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-ext 2750
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-in 3728  df-ss 3735
This theorem is referenced by:  bnj1212  31202  bnj1173  31402  bnj1296  31421  bnj1408  31436  bnj1452  31452  bnj1523  31471
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