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Theorem syl9 66
Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.)
Hypotheses
Ref Expression
syl9.1 (φ → (ψχ))
syl9.2 (θ → (χτ))
Assertion
Ref Expression
syl9 (φ → (θ → (ψτ)))

Proof of Theorem syl9
StepHypRef Expression
1 syl9.1 . 2 (φ → (ψχ))
2 syl9.2 . . 3 (θ → (χτ))
32a1i 9 . 2 (φ → (θ → (χτ)))
41, 3syl5d 62 1 (φ → (θ → (ψτ)))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  syl9r  67  com23  72  sylan9  389  pm4.79dc  808  pclem6  1264  bilukdc  1284  sbequi  1717  reuss2  3211  reupick  3215  elres  4589  funimass4  5167  fliftfun  5379  elabgf2  9254  bj-rspgt  9260
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