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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 (𝜑 → (𝜓𝜑))
Assertion
Ref Expression
ibir (𝜑𝜓)

Proof of Theorem ibir
StepHypRef Expression
1 ibir.1 . . 3 (𝜑 → (𝜓𝜑))
21bicomd 141 . 2 (𝜑 → (𝜑𝜓))
32ibi 176 1 (𝜑𝜓)
Colors of variables: wff set class
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  704  elpr2  3614  eusv2i  4455  ffdm  5386  ov  5993  ovg  6012  nnacl  6480  elpm2r  6665  ltnqpri  7592  ltxrlt  8022  uzaddcl  9585  expcllem  10530  qexpclz  10540  1exp  10548  facnn  10706  fac0  10707  fac1  10708  bcn2  10743  znnen  12398
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