Theorem dtrucor2 4901

Description: The theorem form of the deduction dtrucor 4900 leads to a contradiction, as mentioned in the "Wrong!" example at mmdeduction.html#bad. (Contributed by NM, 20-Oct-2007.)

Hypothesis

Ref	Expression
dtrucor2.1	|- ( x = y -> x =/= y )

Assertion

Ref	Expression
dtrucor2	|- ( ph /\ -. ph )

Proof of Theorem dtrucor2

Step	Hyp	Ref	Expression
1		ax6e 2250	. 2 |- E. x x = y
2		dtrucor2.1	. . . . 5 |- ( x = y -> x =/= y )
3	2	necon2bi 2824	. . . 4 |- ( x = y -> -. x = y )
4		pm2.01 180	. . . 4 |- ( ( x = y -> -. x = y ) -> -. x = y )
5	3, 4	ax-mp 5	. . 3 |- -. x = y
6	5	nex 1731	. 2 |- -. E. x x = y
7	1, 6	pm2.24ii 117	1 |- ( ph /\ -. ph )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384   E.wex 1704   =/= wne 2794

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-ne 2795

This theorem is referenced by: (None)