Theorem necon3bbii 2031

Description: Deduction from equality to inequality.

Hypothesis

Ref	Expression
necon3bbii.1	|- (ph <-> A = B)

Assertion

Ref	Expression
necon3bbii	|- (-. ph <-> A =/= B)

Proof of Theorem necon3bbii

Step	Hyp	Ref	Expression
1		necon3bbii.1	. . . 4 |- (ph <-> A = B)
2	1	bicomi 189	. . 3 |- (A = B <-> ph)
3	2	necon3abii 2030	. 2 |- (A =/= B <-> -. ph)
4	3	bicomi 189	1 |- (-. ph <-> A =/= B)

Syntax hints:  -. wn 2   <-> wb 163   = wceq 1298   =/= wne 2017

This theorem is referenced by:  nssinpss 2824  tfi 3937  oelim2 5270  bcthlem9 9285  shne0i 11004  pjneli 11303  bnj158 12483  dffr5 13831  wfi 13915  frind 13939  ellimits 14079  cnfilca 14927  elicc3 15362  compfipin0 15436  ist1-2 15542  ordintdif 16440

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-ne 2019

Copyright terms: Public domain