Theorem ibd 258

Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. Deduction associated with ibi 256. (Contributed by NM, 26-Jun-2004.)

Hypothesis

Ref	Expression
ibd.1	|- ( ph -> ( ps -> ( ps <-> ch ) ) )

Assertion

Ref	Expression
ibd	|- ( ph -> ( ps -> ch ) )

Proof of Theorem ibd

Step	Hyp	Ref	Expression
1		ibd.1	. 2 |- ( ph -> ( ps -> ( ps <-> ch ) ) )
2		biimp 205	. 2 |- ( ( ps <-> ch ) -> ( ps -> ch ) )
3	1, 2	syli 39	1 |- ( ph -> ( ps -> ch ) )

Syntax hints:   -> wi 4   <-> wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  sssn  4358  unblem2  8213  atcv0eq  29238  atcv1  29239  atomli  29241  atcvatlem  29244  ibdr  34142