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Theorem 3anbi1d 1222
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 165 . 2 (𝜑 → (𝜃𝜃))
31, 23anbi12d 1219 1 (𝜑 → ((𝜓𝜃𝜏) ↔ (𝜒𝜃𝜏)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  vtocl3gaf  2639  ordsoexmid  4313  genpelxp  6666
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