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Theorem simplbi2 367
Description: Deduction eliminating a conjunct. (Contributed by Alan Sare, 31-Dec-2011.)
Hypothesis
Ref Expression
pm3.26bi2.1 (φ ↔ (ψ χ))
Assertion
Ref Expression
simplbi2 (ψ → (χφ))

Proof of Theorem simplbi2
StepHypRef Expression
1 pm3.26bi2.1 . . 3 (φ ↔ (ψ χ))
21biimpri 124 . 2 ((ψ χ) → φ)
32ex 108 1 (ψ → (χφ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.62dc  852  pm5.63dc  853  simplbi2com  1333  reuss2  3214  elni2  6302  elfz0ubfz0  8844  elfzmlbp  8852  fzo1fzo0n0  8901  elfzo0z  8902  fzofzim  8906  elfzodifsumelfzo  8919  ialgcvga  9337
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