Theorem mtbi 594

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 124	. 2 |- (ps -> ph)
4	1, 3	mto 587	1 |- -. ps

Syntax hints:  -. wn 3   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  mtbir  595  vprc  3879  vnex  3881  onsucelsucexmid  4215  dtruex  4237  dmsn0  4731  bj-vprc  9351  bj-vnex  9353