Theorem bj-dtrucor2v 31416

Description: Version of dtrucor2 4634 with a dv condition, which does not require ax-13 2091 (nor ax-4 1682, ax-5 1758, ax-7 1851, ax-12 1933). (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-dtrucor2v.1	|- ( x = y -> x =/= y )

Assertion

Ref	Expression
bj-dtrucor2v	|- ( ph /\ -. ph )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem bj-dtrucor2v

Step	Hyp	Ref	Expression
1		ax6ev 1807	. 2 |- E. x x = y
2		bj-dtrucor2v.1	. . . . 5 |- ( x = y -> x =/= y )
3	2	necon2bi 2654	. . . 4 |- ( x = y -> -. x = y )
4		pm2.01 172	. . . 4 |- ( ( x = y -> -. x = y ) -> -. x = y )
5	3, 4	ax-mp 5	. . 3 |- -. x = y
6	5	nex 1678	. 2 |- -. E. x x = y
7	1, 6	pm2.24ii 136	1 |- ( ph /\ -. ph )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 371   E.wex 1663   =/= wne 2622

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-6 1805

This theorem depends on definitions:  df-bi 189  df-ex 1664  df-ne 2624

This theorem is referenced by: (None)