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Theorem 3anbi1d 1294
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 → ((𝜓𝜃𝜏) ↔ (𝜒𝜃𝜏)))

Proof of Theorem 3anbi1d
StepHypRef Expression
1 3anbi1d.1 . 2 (𝜑 → (𝜓𝜒))
2 biidd 171 . 2 (𝜑 → (𝜃𝜃))
31, 23anbi12d 1291 1 (𝜑 → ((𝜓𝜃𝜏) ↔ (𝜒𝜃𝜏)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  w3a 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  vtocl3gaf  2755  ordsoexmid  4477  genpelxp  7331
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