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Theorem bnj1213 31176
 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 3742 1 (𝜃𝑥𝐵)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2139   ⊆ wss 3715 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-in 3722  df-ss 3729 This theorem is referenced by:  bnj1212  31177  bnj1173  31377  bnj1296  31396  bnj1408  31411  bnj1452  31427  bnj1523  31446
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