Theorem bnj226 12516

Description: First-order logic and set theory.

Hypothesis

Ref	Expression
bnj226.1	|- B C_ C

Assertion

Ref	Expression
bnj226	|- U_x e. A B C_ C

Distinct variable group:   x,C

Proof of Theorem bnj226

Step	Hyp	Ref	Expression
1		bnj226.1	. . 3 |- B C_ C
2	1	ax-gen 1305	. 2 |- A.x B C_ C
3	2	bnj225 12514	1 |- U_x e. A B C_ C

Syntax hints:   C_ wss 2593  U_ciun 3255

This theorem is referenced by:  bnj229 13253  bnj1128 13428

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-ral 2109  df-rex 2110  df-v 2294  df-in 2603  df-ss 2605  df-iun 3257

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