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  706  elpr2  3665  eusv2i  4520  ffdm  5466  ov  6088  ovg  6108  nnacl  6589  elpm2r  6776  ltnqpri  7742  ltxrlt  8173  uzaddcl  9742  expcllem  10732  qexpclz  10742  1exp  10750  facnn  10909  fac0  10910  fac1  10911  bcn2  10946  hash2en  11025  znnen  12884  zrhval  14494