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Theorem syl133anc 1205
 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)
syl133anc.8 ((ψ (χ θ τ) (η ζ σ)) → ρ)
Assertion
Ref Expression
syl133anc (φρ)

Proof of Theorem syl133anc
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 . . 3 (φη)
6 sylXanc.6 . . 3 (φζ)
7 sylXanc.7 . . 3 (φσ)
85, 6, 73jca 1132 . 2 (φ → (η ζ σ))
9 syl133anc.8 . 2 ((ψ (χ θ τ) (η ζ σ)) → ρ)
101, 2, 3, 4, 8, 9syl131anc 1195 1 (φρ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ 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:  syl233anc  1211
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