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Theorem syl323anc 1212
 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)
sylXanc.6 (φζ)
sylXanc.7 (φσ)
sylXanc.8 (φρ)
syl323anc.9 (((ψ χ θ) (τ η) (ζ σ ρ)) → μ)
Assertion
Ref Expression
syl323anc (φμ)

Proof of Theorem syl323anc
StepHypRef Expression
1 sylXanc.1 . 2 (φψ)
2 sylXanc.2 . 2 (φχ)
3 sylXanc.3 . 2 (φθ)
4 sylXanc.4 . . 3 (φτ)
5 sylXanc.5 . . 3 (φη)
64, 5jca 518 . 2 (φ → (τ η))
7 sylXanc.6 . 2 (φζ)
8 sylXanc.7 . 2 (φσ)
9 sylXanc.8 . 2 (φρ)
10 syl323anc.9 . 2 (((ψ χ θ) (τ η) (ζ σ ρ)) → μ)
111, 2, 3, 6, 7, 8, 9, 10syl313anc 1206 1 (φμ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∧ 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: (None)
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