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Theorem syl3an2br 1174
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.)
Hypotheses
Ref Expression
syl3an2br.1 (χφ)
syl3an2br.2 ((ψ χ θ) → τ)
Assertion
Ref Expression
syl3an2br ((ψ φ θ) → τ)

Proof of Theorem syl3an2br
StepHypRef Expression
1 syl3an2br.1 . . 3 (χφ)
21biimpri 124 . 2 (φχ)
3 syl3an2br.2 . 2 ((ψ χ θ) → τ)
42, 3syl3an2 1168 1 ((ψ φ θ) → τ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   w3a 884
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 886
This theorem is referenced by: (None)
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