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Theorem a1bi 351
Description: Inference rule introducing a theorem as an antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 11-Nov-2012.)
Hypothesis
Ref Expression
a1bi.1 𝜑
Assertion
Ref Expression
a1bi (𝜓 ↔ (𝜑𝜓))

Proof of Theorem a1bi
StepHypRef Expression
1 a1bi.1 . 2 𝜑
2 biimt 349 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
31, 2ax-mp 5 1 (𝜓 ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197
This theorem is referenced by:  mt2bi  352  pm4.83  990  trut  1532  equsalvw  1977  equsalv  2146  equsalhw  2161  equsal  2327  sbequ8ALT  2435  ralv  3250  relop  5305  acsfn0  16368  cmpsub  21251  ballotlemodife  30687  bj-ssb1  32758  bj-ralvw  32990  wl-equsald  33455  lub0N  34794  glb0N  34798
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