Theorem ibd 593

Description: Deduction that converts a biconditional implied by one of its arguments, into an implication.

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		ibib 589	. 2 |- ((ps -> ch) <-> (ps -> (ps <-> ch)))
3	1, 2	sylibr 200	1 |- (ph -> (ps -> ch))

Syntax hints:   -> wi 3   <-> wb 146

This theorem is referenced by:  oibabs 653  sssn 2471  reuuni4 2884  unblem2 4531  alephon 4852  atcv0eq 10297  atcv1t 10298  atoml 10300  atcvatlem 10303

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