Theorem mtbi 191

Description: An inference from a biconditional, related to modus tollens.

Hypotheses

Ref	Expression
mtbi.1	|- -. ph
mtbi.2	|- (ph <-> ps)

Assertion

Ref	Expression
mtbi	|- -. ps

Proof of Theorem mtbi

Step	Hyp	Ref	Expression
1		mtbi.1	. 2 |- -. ph
2		mtbi.2	. . 3 |- (ph <-> ps)
3	2	negbii 187	. 2 |- (-. ph <-> -. ps)
4	1, 3	mpbi 189	1 |- -. ps

Syntax hints:  -. wn 2   <-> wb 146

This theorem is referenced by:  nvelv 2708  vnex 2710  opprc1b 2791  opthwiener 2802  dmsnsn0 3320  alephprc 4873  unialeph 4875  sinhalfpilem 8617

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 147

Copyright terms: Public domain