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Theorem syl9r 67
Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
syl9r.1 (φ → (ψχ))
syl9r.2 (θ → (χτ))
Assertion
Ref Expression
syl9r (θ → (φ → (ψτ)))

Proof of Theorem syl9r
StepHypRef Expression
1 syl9r.1 . . 3 (φ → (ψχ))
2 syl9r.2 . . 3 (θ → (χτ))
31, 2syl9 66 . 2 (φ → (θ → (ψτ)))
43com12 27 1 (θ → (φ → (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:  sylan9r  390  pm2.85dc  810  looinvdc  820  pclem6  1264  nfimd  1474  19.23t  1564  fununi  4910  dfimafn  5165  funimass3  5226  nnsub  7733
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