Theorem dtrucor 4685

Description: Corollary of dtru 4643. 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 4686. (Contributed by NM, 27-Jun-2002.)

Hypothesis

Ref	Expression
dtrucor.1

Assertion

Ref	Expression
dtrucor

Distinct variable group:   ,

Proof of Theorem dtrucor

Step	Hyp	Ref	Expression
1		dtru 4643	. . 3
2	1	pm2.21i 131	. 2
3		dtrucor.1	. 2
4	2, 3	mpg 1620	1

Syntax hints:  A.wal 1393  =/=wne 2652

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-nul 4581  ax-pow 4630

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617