Theorem mtbi 676

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 668	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 619  ax-in2 620

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  mtbir  677  vnex  4220  onsucelsucexmid  4628  dtruex  4657  dmsn0  5204  php5  7043  exmidonfinlem  7403  ndvdsi  12493  nprmi  12695  dec2dvds  12983  dec5dvds2  12985  unennn  13017  bj-vprc  16491  bj-vnex  16493  trirec0xor  16649