Theorem dtrucor 3518

Description: Corollary of dtru 3498. This example illustrates the danger of blindly trusting the standard Deduction Theorem without accounting for free variables: the theorem form of this deduction is not valid, as shown by dtrucor2 3519.

Hypothesis

Ref	Expression
dtrucor.1	|- x = y

Assertion

Ref	Expression
dtrucor	|- x =/= y

Distinct variable group:   x,y

Proof of Theorem dtrucor

Step	Hyp	Ref	Expression
1		dtru 3498	. . 3 |- -. A.x x = y
2	1	pm2.21i 93	. 2 |- (A.x x = y -> x =/= y)
3		dtrucor.1	. 2 |- x = y
4	2, 3	mpg 1332	1 |- x =/= y

Syntax hints:  A.wal 1296   = wceq 1298   =/= wne 2017

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-nul 3445  ax-pow 3481

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

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