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Theorem syl8 65
Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994.) (Proof shortened by Wolf Lammen, 3-Aug-2012.)
Hypotheses
Ref Expression
syl8.1 (φ → (ψ → (χθ)))
syl8.2 (θτ)
Assertion
Ref Expression
syl8 (φ → (ψ → (χτ)))

Proof of Theorem syl8
StepHypRef Expression
1 syl8.1 . 2 (φ → (ψ → (χθ)))
2 syl8.2 . . 3 (θτ)
32a1i 9 . 2 (φ → (θτ))
41, 3syl6d 64 1 (φ → (ψ → (χτ)))
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:  com45  83  syl8ib  155  imp5a  340  con4biddc  753  3exp  1102  suctr  4124  ssorduni  4179  qreccl  8351  bj-inf2vnlem2  9431
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