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Theorem simplbi2 385
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 133 . 2 ((𝜓𝜒) → 𝜑)
32ex 115 1 (𝜓 → (𝜒𝜑))
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  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  pm5.62dc  945  pm5.63dc  946  simplbi2com  1444  reuss2  3417  elni2  7315  elpq  9650  elfz0ubfz0  10127  elfzmlbp  10134  fzo1fzo0n0  10185  elfzo0z  10186  fzofzim  10190  elfzodifsumelfzo  10203  p1modz1  11803  dfgcd2  12017  algcvga  12053  pcprendvds  12292
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