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Theorem simprbda 383
Description: Deduction eliminating a conjunct. (Contributed by NM, 22-Oct-2007.)
Hypothesis
Ref Expression
pm3.26bda.1 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
Assertion
Ref Expression
simprbda ((𝜑𝜓) → 𝜒)

Proof of Theorem simprbda
StepHypRef Expression
1 pm3.26bda.1 . . 3 (𝜑 → (𝜓 ↔ (𝜒𝜃)))
21biimpa 296 . 2 ((𝜑𝜓) → (𝜒𝜃))
32simpld 112 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  elrabi  2890  cvgratz  11521  tg1  13219  cldss  13265  cnf2  13365  cncnp  13390  blgt0  13562  xblss2ps  13564  xblss2  13565  dvcnp2cntop  13823
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