Theorem bnj931 34905

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 ∪ 𝐶)

Assertion

Ref	Expression
bnj931	⊢ 𝐵 ⊆ 𝐴

Proof of Theorem bnj931

Step	Hyp	Ref	Expression
1		ssun1 4129	. 2 ⊢ 𝐵 ⊆ (𝐵 ∪ 𝐶)
2		bnj931.1	. 2 ⊢ 𝐴 = (𝐵 ∪ 𝐶)
3	1, 2	sseqtrri 3982	1 ⊢ 𝐵 ⊆ 𝐴

Syntax hints:   = wceq 1542   ∪ cun 3898   ⊆ wss 3900

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2714  df-cleq 2727  df-clel 2810  df-v 3441  df-un 3905  df-ss 3917

This theorem is referenced by:  bnj945  34908  bnj545  35030  bnj548  35032  bnj570  35040  bnj929  35071  bnj1136  35132  bnj1408  35171  bnj1442  35184