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Theorem 3anibar 1221
Description: Remove a hypothesis from the second member of a biimplication. (Contributed by FL, 22-Jul-2008.)
Hypothesis
Ref Expression
3anibar.1 ((𝜑𝜓𝜒) → (𝜃 ↔ (𝜒𝜏)))
Assertion
Ref Expression
3anibar ((𝜑𝜓𝜒) → (𝜃𝜏))

Proof of Theorem 3anibar
StepHypRef Expression
1 simp3 1055 . 2 ((𝜑𝜓𝜒) → 𝜒)
2 3anibar.1 . 2 ((𝜑𝜓𝜒) → (𝜃 ↔ (𝜒𝜏)))
31, 2mpbirand 528 1 ((𝜑𝜓𝜒) → (𝜃𝜏))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wa 382  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by:  cpmatel  20282  neiint  20665  islinindfiss  42014
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