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Theorem 3simpb 990
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 981 . 2 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
2 3simpa 989 . 2 ((𝜑𝜒𝜓) → (𝜑𝜒))
31, 2sylbi 120 1 ((𝜑𝜓𝜒) → (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 973
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 975
This theorem is referenced by:  3adant2  1011  3adantl2  1149  3adantr2  1152  enq0tr  7383  ixxssixx  9846  rebtwn2zlemshrink  10197  zsumdc  11334  muldvds1  11765  dvds2add  11774  dvds2sub  11775  dvdstr  11777  pw2dvdslemn  12106  ctinf  12372  mndissubm  12683
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