Theorem mtbi 671

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 133	. 2 |- ( ps -> ph )
4	1, 3	mto 663	1 |- -. ps

Syntax hints:   -. wn 3   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  mtbir  672  vnex  4164  onsucelsucexmid  4566  dtruex  4595  dmsn0  5137  php5  6919  exmidonfinlem  7260  ndvdsi  12098  nprmi  12292  dec2dvds  12580  dec5dvds2  12582  unennn  12614  bj-vprc  15542  bj-vnex  15544  trirec0xor  15689