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Theorem 3simpb 953
Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3simpb ((φ ψ χ) → (φ χ))

Proof of Theorem 3simpb
StepHypRef Expression
1 3ancomb 943 . 2 ((φ ψ χ) ↔ (φ χ ψ))
2 3simpa 952 . 2 ((φ χ ψ) → (φ χ))
31, 2sylbi 187 1 ((φ ψ χ) → (φ 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:  3adant2  974  3adantl2  1112  3adantr2  1115
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