Theorem dvdemo2 3521

Description: Demonstration of a theorem that requires x and z to be distinct, but no others. Compare dvdemo1 3520.

Assertion

Ref	Expression
dvdemo2	|- E.x(x = y -> z e. x)

Distinct variable group:   x,z

Proof of Theorem dvdemo2

Step	Hyp	Ref	Expression
1		el 3485	. 2 |- E.x z e. x
2		ax-1 4	. . 3 |- (z e. x -> (x = y -> z e. x))
3	2	eximi 1387	. 2 |- (E.x z e. x -> E.x(x = y -> z e. x))
4	1, 3	ax-mp 7	1 |- E.x(x = y -> z e. x)

Syntax hints:   -> wi 3   = wceq 1298   e. wcel 1300  E.wex 1326

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-12 1310  ax-13 1311  ax-14 1312  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-pow 3481

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327

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