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Theorem simplbi2com 1312
Description: A deduction eliminating a conjunct, similar to simplbi2 367. (Contributed by Alan Sare, 22-Jul-2012.) (Proof shortened by Wolf Lammen, 10-Nov-2012.)
Hypothesis
Ref Expression
simplbi2com.1 (φ ↔ (ψ χ))
Assertion
Ref Expression
simplbi2com (χ → (ψφ))

Proof of Theorem simplbi2com
StepHypRef Expression
1 simplbi2com.1 . . 3 (φ ↔ (ψ χ))
21simplbi2 367 . 2 (ψ → (χφ))
32com12 27 1 (χ → (ψφ))
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:  mo2r  1934  mo3h  1935  elres  4573  xpidtr  4642
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