Theorem bnj1424 13119

Description: First-order logic and set theory.

Hypothesis

Ref	Expression
bnj1424.1	|- A = (B u. C)

Assertion

Ref	Expression
bnj1424	|- (D e. A -> (D e. B \/ D e. C))

Proof of Theorem bnj1424

Step	Hyp	Ref	Expression
1		bnj1424.1	. . 3 |- A = (B u. C)
2	1	bnj1138 12936	. 2 |- (D e. A <-> (D e. B \/ D e. C))
3	2	biimpi 168	1 |- (D e. A -> (D e. B \/ D e. C))

Syntax hints:   -> wi 3   \/ wo 239   = wceq 1298   e. wcel 1300   u. cun 2591

This theorem is referenced by:  bnj1440 13543  bnj1462 13546

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-v 2294  df-un 2600

Copyright terms: Public domain