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Theorem a1bi 353
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 351 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
31, 2ax-mp 5 1 (𝜓 ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 197
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 198
This theorem is referenced by:  mt2bi  354  pm4.83  1039  trut  1644  equsalvw  2100  equsalv  2276  equsalhwOLD  2299  equsal  2458  sbequ8ALT  2566  ralv  3413  relop  5474  acsfn0  16521  cmpsub  21413  ballotlemodife  30880  bj-ssb1  32944  bj-ralvw  33168  wl-equsald  33634  lub0N  34964  glb0N  34968
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