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Theorem ibir 175
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
StepHypRef Expression
1 ibir.1 . . 3  |-  ( ph  ->  ( ps  <->  ph ) )
21bicomd 139 . 2  |-  ( ph  ->  ( ph  <->  ps )
)
32ibi 174 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm5.21nii  653  elpr2  3439  eusv2i  4234  ffdm  5113  ov  5672  ovg  5691  nnacl  6145  ltnqpri  6882  ltxrlt  7281  uzaddcl  8791  expcllem  9620  qexpclz  9630  1exp  9638  facnn  9787  fac0  9788  fac1  9789  bcn2  9824  znnen  10802
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