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Theorem bnj21 28788
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 3388 . 2  |-  { x  e.  A  |  ph }  C_  A
31, 2eqsstri 3338 1  |-  B  C_  A
Colors of variables: wff set class
Syntax hints:    = wceq 1649   {crab 2670    C_ wss 3280
This theorem is referenced by:  bnj1212  28877  bnj213  28959  bnj1286  29094  bnj1312  29133  bnj1523  29146
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rab 2675  df-in 3287  df-ss 3294
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