Metamath Proof Explorer


Theorem dtrucor

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

Ref Expression
Hypothesis dtrucor.1
|- x = y
Assertion dtrucor
|- x =/= y

Proof

Step Hyp Ref Expression
1 dtrucor.1
 |-  x = y
2 dtruALT2
 |-  -. A. x x = y
3 2 pm2.21i
 |-  ( A. x x = y -> x =/= y )
4 3 1 mpg
 |-  x =/= y