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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
syl8.2
Assertion
Ref Expression
syl8

Proof of Theorem syl8
StepHypRef Expression
1 syl8.1 . 2
2 syl8.2 . . 3
32a1i 10 . 2
41, 3syl6d 64 1
Colors of variables: wff setvar class
Syntax hints:   wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
This theorem is referenced by:  com45  83  syl8ib  222  imp5a  581  3exp  1150  nclenn  6249
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