Theorem bnj213 30952

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Assertion

Ref	Expression
bnj213	|- pred ( X , A , R ) C_ A

Proof of Theorem bnj213

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-bnj14 30755	. 2 |- pred ( X , A , R ) = { y e. A | y R X }
2	1	ssrab3 3688	1 |- pred ( X , A , R ) C_ A

Syntax hints:   C_ wss 3574   class class class wbr 4653   predc-bnj14 30754

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-in 3581  df-ss 3588  df-bnj14 30755

This theorem is referenced by:  bnj229  30954  bnj517  30955  bnj1128  31058  bnj1145  31061  bnj1137  31063  bnj1408  31104  bnj1417  31109  bnj1523  31139