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Theorem syl231anc 1202
 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)
syl231anc.7 (((ψ χ) (θ τ η) ζ) → σ)
Assertion
Ref Expression
syl231anc (φσ)

Proof of Theorem syl231anc
StepHypRef Expression
1 sylXanc.1 . . 3 (φψ)
2 sylXanc.2 . . 3 (φχ)
31, 2jca 518 . 2 (φ → (ψ χ))
4 sylXanc.3 . 2 (φθ)
5 sylXanc.4 . 2 (φτ)
6 sylXanc.5 . 2 (φη)
7 sylXanc.6 . 2 (φζ)
8 syl231anc.7 . 2 (((ψ χ) (θ τ η) ζ) → σ)
93, 4, 5, 6, 7, 8syl131anc 1195 1 (φσ)
 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:  syl232anc  1209
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