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Theorem syl321anc 1204
Description: Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)
Hypotheses
Ref Expression
sylXanc.1 (φψ)
sylXanc.2 (φχ)
sylXanc.3 (φθ)
sylXanc.4 (φτ)
sylXanc.5 (φη)
sylXanc.6 (φζ)
syl321anc.7 (((ψ χ θ) (τ η) ζ) → σ)
Assertion
Ref Expression
syl321anc (φσ)

Proof of Theorem syl321anc
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 syl321anc.7 . 2 (((ψ χ θ) (τ η) ζ) → σ)
91, 2, 3, 6, 7, 8syl311anc 1196 1 (φσ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   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:  syl322anc  1210
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