Theorem ibir 593

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

Hypothesis

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

Assertion

Ref	Expression
ibir	|- (ph -> ps)

Proof of Theorem ibir

Step	Hyp	Ref	Expression
1		ibir.1	. . 3 |- (ph -> (ps <-> ph))
2	1	bicomd 521	. 2 |- (ph -> (ph <-> ps))
3	2	ibi 592	1 |- (ph -> ps)

Syntax hints:   -> wi 3   <-> wb 146

This theorem is referenced by:  elpr2 2425  ffdm 3639  oprabval 4023  oacl 4170  nnacl 4229  cdafi 4936  nnnn0addclt 6125  uzaddclt 6449  expcllem 6575  pjin 9644

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