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Theorem 3anbi1d 1210
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 161 . 2 (φ → (θθ))
31, 23anbi12d 1207 1 (φ → ((ψ θ τ) ↔ (χ θ τ)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   w3a 884
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 886
This theorem is referenced by:  vtocl3gaf  2616  ordsoexmid  4240  genpelxp  6494
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