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Theorem sylanbr 273
Description: A syllogism inference. (Contributed by NM, 18-May-1994.)
Hypotheses
Ref Expression
sylanbr.1 (𝜓𝜑)
sylanbr.2 ((𝜓𝜒) → 𝜃)
Assertion
Ref Expression
sylanbr ((𝜑𝜒) → 𝜃)

Proof of Theorem sylanbr
StepHypRef Expression
1 sylanbr.1 . . 3 (𝜓𝜑)
21biimpri 128 . 2 (𝜑𝜓)
3 sylanbr.2 . 2 ((𝜓𝜒) → 𝜃)
42, 3sylan 271 1 ((𝜑𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  syl2anbr  280  mosubt  2741  xpiindim  4501  funfvdm  5264  caovimo  5722  tfrlem7  5964  iinerm  6209  expclzaplem  9444  expgt0  9453  expge0  9456  expge1  9457
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