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Theorem 3simpc 954
Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
3simpc ((φ ψ χ) → (ψ χ))

Proof of Theorem 3simpc
StepHypRef Expression
1 3anrot 939 . 2 ((φ ψ χ) ↔ (ψ χ φ))
2 3simpa 952 . 2 ((ψ χ φ) → (ψ χ))
31, 2sylbi 187 1 ((φ ψ χ) → (ψ χ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  simp3  957  3adant1  973  3adantl1  1111  3adantr1  1114  eupickb  2269
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