Theorem bnj931 30841

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

Hypothesis

Ref	Expression
bnj931.1	|- A = ( B u. C )

Assertion

Ref	Expression
bnj931	|- B C_ A

Proof of Theorem bnj931

Step	Hyp	Ref	Expression
1		ssun1 3776	. 2 |- B C_ ( B u. C )
2		bnj931.1	. 2 |- A = ( B u. C )
3	1, 2	sseqtr4i 3638	1 |- B C_ A

Syntax hints:   = wceq 1483   u. cun 3572   C_ wss 3574

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-v 3202  df-un 3579  df-in 3581  df-ss 3588

This theorem is referenced by:  bnj945  30844  bnj545  30965  bnj548  30967  bnj570  30975  bnj929  31006  bnj1136  31065  bnj1408  31104  bnj1442  31117