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Theorem ibir 166
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 129 . 2 (φ → (φψ))
32ibi 165 1 (φψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.21nii  619  elpr2  3386  eusv2i  4153  ffdm  5004  ov  5562  ovg  5581  nnacl  5998  ltxrlt  6842  uzaddcl  8265  expcllem  8880  qexpclz  8890  1exp  8898
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