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Theorem syld3an2 1263
Description: A syllogism inference. (Contributed by NM, 20-May-2007.)
Hypotheses
Ref Expression
syld3an2.1 ((𝜑𝜒𝜃) → 𝜓)
syld3an2.2 ((𝜑𝜓𝜃) → 𝜏)
Assertion
Ref Expression
syld3an2 ((𝜑𝜒𝜃) → 𝜏)

Proof of Theorem syld3an2
StepHypRef Expression
1 syld3an2.1 . . . 4 ((𝜑𝜒𝜃) → 𝜓)
213com23 1187 . . 3 ((𝜑𝜃𝜒) → 𝜓)
3 syld3an2.2 . . . 4 ((𝜑𝜓𝜃) → 𝜏)
433com23 1187 . . 3 ((𝜑𝜃𝜓) → 𝜏)
52, 4syld3an3 1261 . 2 ((𝜑𝜃𝜒) → 𝜏)
653com23 1187 1 ((𝜑𝜒𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 962
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 964
This theorem is referenced by:  nppcan2  8000  nnncan  8004  nnncan2  8006  ltdivmul  8641  ledivmul  8642  ltdiv23  8657  lediv23  8658  dvdssub2  11542  dvdsgcdb  11708  lcmdvdsb  11772
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