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Theorem iba 298
Description: Introduction of antecedent as conjunct. Theorem *4.73 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-Mar-1994.) (Revised by NM, 24-Mar-2013.)
Assertion
Ref Expression
iba (𝜑 → (𝜓 ↔ (𝜓𝜑)))

Proof of Theorem iba
StepHypRef Expression
1 pm3.21 262 . 2 (𝜑 → (𝜓 → (𝜓𝜑)))
2 simpl 108 . 2 ((𝜓𝜑) → 𝜓)
31, 2impbid1 141 1 (𝜑 → (𝜓 ↔ (𝜓𝜑)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  biantru  300  biantrud  302  ancrb  320  rbaibd  909  dedlem0a  952  fvopab6  5517  fressnfv  5607  tpostpos  6161  nnmword  6414  unfiexmid  6806  ltmpig  7159  mul0eqap  8443  sup3exmid  8727  xrmaxiflemcom  11030
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