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Theorem imbi1 335
Description: Theorem *4.84 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
imbi1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))

Proof of Theorem imbi1
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
21imbi1d 329 1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194
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 195
This theorem is referenced by:  imbi1i  337  wl-nanbi1  32275  wl-nanbi2  32276  ifpbi1  36637  3impexpVD  37909  ancomstVD  37919  onfrALTVD  37945  hbimpgVD  37958  hbexgVD  37960  ax6e2ndeqVD  37963  ax6e2ndeqALT  37985
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