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Theorem bnj21 28743
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj21.1  |-  B  =  { x  e.  A  |  ph }
Assertion
Ref Expression
bnj21  |-  B  C_  A
Distinct variable group:    x, A
Allowed substitution hints:    ph( x)    B( x)

Proof of Theorem bnj21
StepHypRef Expression
1 bnj21.1 . 2  |-  B  =  { x  e.  A  |  ph }
2 ssrab2 3258 . 2  |-  { x  e.  A  |  ph }  C_  A
31, 2eqsstri 3208 1  |-  B  C_  A
Colors of variables: wff set class
Syntax hints:    = wceq 1623   {crab 2547    C_ wss 3152
This theorem is referenced by:  bnj1212  28832  bnj213  28914  bnj1286  29049  bnj1312  29088  bnj1523  29101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-in 3159  df-ss 3166
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