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Theorem simp1bi 905
Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
3simp1bi.1 (φ ↔ (ψ χ θ))
Assertion
Ref Expression
simp1bi (φψ)

Proof of Theorem simp1bi
StepHypRef Expression
1 3simp1bi.1 . . 3 (φ ↔ (ψ χ θ))
21biimpi 113 . 2 (φ → (ψ χ θ))
32simp1d 902 1 (φψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   w3a 871
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99
This theorem depends on definitions:  df-bi 110  df-3an 873
This theorem is referenced by:  limord  4077  smores2  5827  smofvon2dm  5829  smofvon  5832  errel  6022
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