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Theorem 3anbi13d 1254
Description: Deduction conjoining and adding a conjunct to equivalences. (Contributed by NM, 8-Sep-2006.)
Hypotheses
Ref Expression
3anbi12d.1 (φ → (ψχ))
3anbi12d.2 (φ → (θτ))
Assertion
Ref Expression
3anbi13d (φ → ((ψ η θ) ↔ (χ η τ)))

Proof of Theorem 3anbi13d
StepHypRef Expression
1 3anbi12d.1 . 2 (φ → (ψχ))
2 biidd 228 . 2 (φ → (ηη))
3 3anbi12d.2 . 2 (φ → (θτ))
41, 2, 33anbi123d 1252 1 (φ → ((ψ η θ) ↔ (χ η τ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   w3a 934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  3anbi3d  1258  ax11wdemo  1723  sfineq1  4526  spaccl  6286  spacind  6287  nchoicelem3  6291
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