Theorem mtbi 659

Description: An inference from a biconditional, related to modus tollens. (Contributed by NM, 15-Nov-1994.) (Proof shortened by Wolf Lammen, 25-Oct-2012.)

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	biimpri 132	. 2 |- ( ps -> ph )
4	1, 3	mto 651	1 |- -. ps

Syntax hints:   -. wn 3   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  mtbir  660  vnex  4059  onsucelsucexmid  4445  dtruex  4474  dmsn0  5006  php5  6752  exmidonfinlem  7049  ndvdsi  11630  nprmi  11805  unennn  11910  bj-vprc  13094  bj-vnex  13096