Theorem mpbidi 207

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994.)

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	biimpd 198	. 2 |- (ph -> (ps -> ch))
4	1, 3	sylcom 25	1 |- (th -> (ph -> ch))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by:  tpid3g  3832  ov3  5600  ovmpt4g  5711