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Theorem syl3anbrc 1136
Description: Syllogism inference. (Contributed by Mario Carneiro, 11-May-2014.)
Hypotheses
Ref Expression
syl3anbrc.1 (φψ)
syl3anbrc.2 (φχ)
syl3anbrc.3 (φθ)
syl3anbrc.4 (τ ↔ (ψ χ θ))
Assertion
Ref Expression
syl3anbrc (φτ)

Proof of Theorem syl3anbrc
StepHypRef Expression
1 syl3anbrc.1 . . 3 (φψ)
2 syl3anbrc.2 . . 3 (φχ)
3 syl3anbrc.3 . . 3 (φθ)
41, 2, 33jca 1132 . 2 (φ → (ψ χ θ))
5 syl3anbrc.4 . 2 (τ ↔ (ψ χ θ))
64, 5sylibr 203 1 (φτ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  sfindbl  4530  vfinspsslem1  4550  pod  5936  fundmen  6043  enmap1  6074  enprmap  6082
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