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  620  elpr2  3397  eusv2i  4187  ffdm  5061  ov  5620  ovg  5639  nnacl  6059  ltnqpri  6692  ltxrlt  7085  uzaddcl  8529  expcllem  9266  qexpclz  9276  1exp  9284