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Theorem fveleq 36434
Description: Please add description here. (Contributed by Jeff Hoffman, 12-Feb-2008.)
Assertion
Ref Expression
fveleq (𝐴 = 𝐵 → ((𝜑 → (𝐹𝐴) ∈ 𝑃) ↔ (𝜑 → (𝐹𝐵) ∈ 𝑃)))

Proof of Theorem fveleq
StepHypRef Expression
1 fveq2 6907 . . 3 (𝐴 = 𝐵 → (𝐹𝐴) = (𝐹𝐵))
21eleq1d 2824 . 2 (𝐴 = 𝐵 → ((𝐹𝐴) ∈ 𝑃 ↔ (𝐹𝐵) ∈ 𝑃))
32imbi2d 340 1 (𝐴 = 𝐵 → ((𝜑 → (𝐹𝐴) ∈ 𝑃) ↔ (𝜑 → (𝐹𝐵) ∈ 𝑃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206   = wceq 1537  wcel 2106  cfv 6563
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571
This theorem is referenced by:  findfvcl  36435
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