Theorem ibir 177

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 141	. 2 |- ( ph -> ( ph <-> ps ) )
3	2	ibi 176	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.21nii  712  elpr2  3713  eusv2i  4578  ffdm  5535  ov  6175  ovg  6195  nnacl  6715  elpm2r  6902  ltnqpri  7911  ltxrlt  8341  uzaddcl  9921  fzspl  10407  expcllem  10916  qexpclz  10926  1exp  10934  facnn  11093  fac0  11094  fac1  11095  bcn2  11130  en1hash  11167  hash2en  11219  znnen  13166  zrhval  14782