Theorem mtbid 713

Description: A deduction from a biconditional, similar to modus tollens.

Hypotheses

Ref	Expression
mtbid.min	|- (ph -> -. ps)
mtbid.maj	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
mtbid	|- (ph -> -. ch)

Proof of Theorem mtbid

Step	Hyp	Ref	Expression
1		mtbid.min	. 2 |- (ph -> -. ps)
2		mtbid.maj	. . 3 |- (ph -> (ps <-> ch))
3	2	biimprd 154	. 2 |- (ph -> (ch -> ps))
4	1, 3	mtod 108	1 |- (ph -> -. ch)

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146

This theorem is referenced by:  axpownd 4933  genpnnp 5088  xrlttrit 5533

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