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Theorem imbi1 336
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 330 1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
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:  imbi1i  338  wl-nanbi1  33430  wl-nanbi2  33431  ifpbi1  38139  3impexpVD  39405  ancomstVD  39415  onfrALTVD  39441  hbimpgVD  39454  hbexgVD  39456  ax6e2ndeqVD  39459  ax6e2ndeqALT  39481
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