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Theorem simplbi2 371
Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011.)
Hypothesis
Ref Expression
pm3.26bi2.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
simplbi2 (𝜓 → (𝜒𝜑))

Proof of Theorem simplbi2
StepHypRef Expression
1 pm3.26bi2.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21biimpri 128 . 2 ((𝜓𝜒) → 𝜑)
32ex 112 1 (𝜓 → (𝜒𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
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
This theorem is referenced by:  pm5.62dc  863  pm5.63dc  864  simplbi2com  1349  reuss2  3245  elni2  6470  elfz0ubfz0  9084  elfzmlbp  9092  fzo1fzo0n0  9141  elfzo0z  9142  fzofzim  9146  elfzodifsumelfzo  9159  ialgcvga  10273
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