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Theorem syl131anc 1195
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)
syl131anc.6 ((ψ (χ θ τ) η) → ζ)
Assertion
Ref Expression
syl131anc (φζ)

Proof of Theorem syl131anc
StepHypRef Expression
1 sylXanc.1 . 2 (φψ)
2 sylXanc.2 . . 3 (φχ)
3 sylXanc.3 . . 3 (φθ)
4 sylXanc.4 . . 3 (φτ)
52, 3, 43jca 1132 . 2 (φ → (χ θ τ))
6 sylXanc.5 . 2 (φη)
7 syl131anc.6 . 2 ((ψ (χ θ τ) η) → ζ)
81, 5, 6, 7syl3anc 1182 1 (φζ)
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:  syl132anc  1200  syl231anc  1202  syl133anc  1205
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