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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
StepHypRef Expression
1 ax6ev 1807 . 2  |-  E. x  x  =  y
2 bj-dtrucor2v.1 . . . . 5  |-  ( x  =  y  ->  x  =/=  y )
32necon2bi 2654 . . . 4  |-  ( x  =  y  ->  -.  x  =  y )
4 pm2.01 172 . . . 4  |-  ( ( x  =  y  ->  -.  x  =  y
)  ->  -.  x  =  y )
53, 4ax-mp 5 . . 3  |-  -.  x  =  y
65nex 1678 . 2  |-  -.  E. x  x  =  y
71, 6pm2.24ii 136 1  |-  ( ph  /\ 
-.  ph )
Colors of variables: wff setvar class
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)
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