Theorem mpbidi 589

Description: A deduction from a biconditional, related to modus ponens.

Hypotheses

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

Assertion

Ref	Expression
mpbidi	|- (th -> (ph -> ch))

Proof of Theorem mpbidi

Step	Hyp	Ref	Expression
1		mpbidi.min	. 2 |- (th -> (ph -> ps))
2		mpbidi.maj	. . 3 |- (ph -> (ps <-> ch))
3	2	pm5.74i 584	. 2 |- ((ph -> ps) <-> (ph -> ch))
4	1, 3	sylib 198	1 |- (th -> (ph -> ch))

Syntax hints:   -> wi 3   <-> wb 146

This theorem is referenced by:  tfrlem5 3915

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  df-an 225

Copyright terms: Public domain