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Theorem syl23anc 1189
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)
syl23anc.6 (((ψ χ) (θ τ η)) → ζ)
Assertion
Ref Expression
syl23anc (φζ)

Proof of Theorem syl23anc
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 syl23anc.6 . 2 (((ψ χ) (θ τ η)) → ζ)
83, 4, 5, 6, 7syl13anc 1184 1 (φζ)
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: (None)
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