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Theorem syl311anc 1196
 Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)
Hypotheses
Ref Expression
sylXanc.1 (φψ)
sylXanc.2 (φχ)
sylXanc.3 (φθ)
sylXanc.4 (φτ)
sylXanc.5 (φη)
syl311anc.6 (((ψ χ θ) τ η) → ζ)
Assertion
Ref Expression
syl311anc (φζ)

Proof of Theorem syl311anc
StepHypRef Expression
1 sylXanc.1 . . 3 (φψ)
2 sylXanc.2 . . 3 (φχ)
3 sylXanc.3 . . 3 (φθ)
41, 2, 33jca 1132 . 2 (φ → (ψ χ θ))
5 sylXanc.4 . 2 (φτ)
6 sylXanc.5 . 2 (φη)
7 syl311anc.6 . 2 (((ψ χ θ) τ η) → ζ)
84, 5, 6, 7syl3anc 1182 1 (φζ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 934 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936 This theorem is referenced by:  syl312anc  1203  syl321anc  1204  syl313anc  1206  syl331anc  1207
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