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Theorem bnj1213 32522
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 3916 1 (𝜃𝑥𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2112  wss 3883
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2114  ax-9 2122  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-ex 1788  df-sb 2073  df-clab 2717  df-cleq 2731  df-clel 2818  df-v 3425  df-in 3890  df-ss 3900
This theorem is referenced by:  bnj1212  32523  bnj1173  32726  bnj1296  32745  bnj1408  32760  bnj1452  32776  bnj1523  32795
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