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Theorem syl113anc 1194
 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)
syl113anc.6 ((ψ χ (θ τ η)) → ζ)
Assertion
Ref Expression
syl113anc (φζ)

Proof of Theorem syl113anc
StepHypRef Expression
1 sylXanc.1 . 2 (φψ)
2 sylXanc.2 . 2 (φχ)
3 sylXanc.3 . . 3 (φθ)
4 sylXanc.4 . . 3 (φτ)
5 sylXanc.5 . . 3 (φη)
63, 4, 53jca 1132 . 2 (φ → (θ τ η))
7 syl113anc.6 . 2 ((ψ χ (θ τ η)) → ζ)
81, 2, 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:  syl123anc  1199  syl213anc  1201
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