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  3655  eusv2i  4502  ffdm  5446  ov  6065  ovg  6085  nnacl  6566  elpm2r  6753  ltnqpri  7707  ltxrlt  8138  uzaddcl  9707  expcllem  10695  qexpclz  10705  1exp  10713  facnn  10872  fac0  10873  fac1  10874  bcn2  10909  hash2en  10988  znnen  12769  zrhval  14379