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Theorem simprbda 380
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 294 . 2 ((𝜑𝜓) → (𝜒𝜃))
32simpld 111 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  elrabi  2810  cvgratz  11269  tg1  12155  cldss  12201  cnf2  12301  cncnp  12326  blgt0  12498  xblss2ps  12500  xblss2  12501  dvcnp2cntop  12759
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