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Theorem imbi2 337
 Description: Theorem *4.85 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 19-May-2013.)
Assertion
Ref Expression
imbi2 ((𝜑𝜓) → ((𝜒𝜑) ↔ (𝜒𝜓)))

Proof of Theorem imbi2
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
21imbi2d 329 1 ((𝜑𝜓) → ((𝜒𝜑) ↔ (𝜒𝜓)))
 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:  relexpindlem  14022  relexpind  14023  ifpbi2  38331  ifpbi3  38332  3impexpbicom  39205  sbcim2g  39268  3impexpbicomVD  39609  sbcim2gVD  39628  csbeq2gVD  39645  con5VD  39653  hbexgVD  39659  ax6e2ndeqVD  39662  2sb5ndVD  39663  ax6e2ndeqALT  39684  2sb5ndALT  39685
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