Theorem imbi2 348

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	⊢ ((𝜑 ↔ 𝜓) → ((𝜒 → 𝜑) ↔ (𝜒 → 𝜓)))

Proof of Theorem imbi2

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	imbi2d 340	1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜒 → 𝜑) ↔ (𝜒 → 𝜓)))

Syntax hints:   → wi 4   ↔ wb 206

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 207

This theorem is referenced by:  imbibi  391  con3ALT  1084  axpr  5433  relexpindlem  15099  relexpind  15100  unielss  43207  ifpbi2  43457  ifpbi3  43458  3impexpbicom  44477  sbcim2g  44536  3impexpbicomVD  44855  sbcim2gVD  44873  csbeq2gVD  44890  con5VD  44898  hbexgVD  44904  ax6e2ndeqVD  44907  2sb5ndVD  44908  ax6e2ndeqALT  44929  2sb5ndALT  44930