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Theorem syl333anc 1214
 Description: A syllogism inference combined with contraction. (Contributed by NM, 10-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)
sylXanc.9 (φμ)
syl333anc.10 (((ψ χ θ) (τ η ζ) (σ ρ μ)) → λ)
Assertion
Ref Expression
syl333anc (φλ)

Proof of Theorem syl333anc
StepHypRef Expression
1 sylXanc.1 . 2 (φψ)
2 sylXanc.2 . 2 (φχ)
3 sylXanc.3 . 2 (φθ)
4 sylXanc.4 . 2 (φτ)
5 sylXanc.5 . 2 (φη)
6 sylXanc.6 . 2 (φζ)
7 sylXanc.7 . . 3 (φσ)
8 sylXanc.8 . . 3 (φρ)
9 sylXanc.9 . . 3 (φμ)
107, 8, 93jca 1132 . 2 (φ → (σ ρ μ))
11 syl333anc.10 . 2 (((ψ χ θ) (τ η ζ) (σ ρ μ)) → λ)
121, 2, 3, 4, 5, 6, 10, 11syl331anc 1207 1 (φλ)
 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: (None)
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