Theorem ibir 166

Description: Inference that converts a biconditional implied by one of its arguments, into an implication. (Contributed by NM, 22-Jul-2004.)

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 129	. 2 |- (ph -> (ph <-> ps))
3	2	ibi 165	1 |- (ph -> ps)

Syntax hints:   -> wi 4   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  pm5.21nii  619  elpr2  3386  eusv2i  4153  ffdm  5004  ov  5562  ovg  5581  nnacl  5998  ltxrlt  6882  uzaddcl  8305  expcllem  8920  qexpclz  8930  1exp  8938