Theorem csbexOLD 2550

Description: The existence of proper substitution into a class.

Hypotheses

Ref	Expression
csbex.1	|- A e. _V
csbex.2	|- B e. _V

Assertion

Ref	Expression
csbexOLD	|- [_A / x]_B e. _V

Proof of Theorem csbexOLD

Step	Hyp	Ref	Expression
1		csbex.1	. 2 |- A e. _V
2		csbex.2	. . 3 |- B e. _V
3	2	ax-gen 1305	. 2 |- A.x B e. _V
4		csbexg 2548	. 2 |- ((A e. _V /\ A.x B e. _V) -> [_A / x]_B e. _V)
5	1, 3, 4	mp2an 761	1 |- [_A / x]_B e. _V

Syntax hints:  A.wal 1296   e. wcel 1300  _Vcvv 2292  [_csb 2540

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-sbc 2454  df-csb 2541

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