Theorem mpbidi 447

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 443	. 2 |- ((ph -> ps) <-> (ph -> ch))
4	1, 3	sylib 173	1 |- (th -> (ph -> ch))

Syntax hints:   -> wi 2   <-> wb 127

This theorem is referenced by:  tfrlem5 2953  pjss1co 5633

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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