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Theorem 3simpb 947
Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3simpb ((𝜑𝜓𝜒) → (𝜑𝜒))

Proof of Theorem 3simpb
StepHypRef Expression
1 3ancomb 938 . 2 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
2 3simpa 946 . 2 ((𝜑𝜒𝜓) → (𝜑𝜒))
31, 2sylbi 120 1 ((𝜑𝜓𝜒) → (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 930
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 932
This theorem is referenced by:  3adant2  968  3adantl2  1106  3adantr2  1109  enq0tr  7143  ixxssixx  9526  rebtwn2zlemshrink  9872  zsumdc  10992  muldvds1  11313  dvds2add  11322  dvds2sub  11323  dvdstr  11325  pw2dvdslemn  11635  ctinf  11735
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