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Theorem 3anbi1d 1256
Description: Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)
Hypothesis
Ref Expression
3anbi1d.1 (φ → (ψχ))
Assertion
Ref Expression
3anbi1d (φ → ((ψ θ τ) ↔ (χ θ τ)))

Proof of Theorem 3anbi1d
StepHypRef Expression
1 3anbi1d.1 . 2 (φ → (ψχ))
2 biidd 228 . 2 (φ → (θθ))
31, 23anbi12d 1253 1 (φ → ((ψ θ τ) ↔ (χ θ τ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   w3a 934
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 177  df-an 360  df-3an 936
This theorem is referenced by:  vtocl3gaf  2923  opkelins2kg  4251  opkelins3kg  4252  opkelsikg  4264  sikss1c1c  4267  brsi  4761  funsi  5520  brsnsi  5773  fnpprod  5843  ovce  6172
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