Theorem ibd 178

Description: Deduction that converts a biconditional implied by one of its arguments, into an implication. (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 118	. 2 |- ( ( ps <-> ch ) -> ( ps -> ch ) )
3	1, 2	syli 37	1 |- ( ph -> ( ps -> ch ) )

This proof depends on syntax axioms:   -> wi 4   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This proof depends on definitions:  df-bi 117

This theorem is used by:  pm5.21ndd  717  oibabs  726  sssnm  3879