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  3695  eusv2i  4558  ffdm  5513  ov  6151  ovg  6171  nnacl  6691  elpm2r  6878  ltnqpri  7874  ltxrlt  8304  uzaddcl  9881  expcllem  10875  qexpclz  10885  1exp  10893  facnn  11052  fac0  11053  fac1  11054  bcn2  11089  en1hash  11125  hash2en  11170  znnen  13099  zrhval  14713