New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  syl132anc GIF version

Theorem syl132anc 1200
 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)
syl132anc.7 ((ψ (χ θ τ) (η ζ)) → σ)
Assertion
Ref Expression
syl132anc (φσ)

Proof of Theorem syl132anc
StepHypRef Expression
1 sylXanc.1 . 2 (φψ)
2 sylXanc.2 . 2 (φχ)
3 sylXanc.3 . 2 (φθ)
4 sylXanc.4 . 2 (φτ)
5 sylXanc.5 . . 3 (φη)
6 sylXanc.6 . . 3 (φζ)
75, 6jca 518 . 2 (φ → (η ζ))
8 syl132anc.7 . 2 ((ψ (χ θ τ) (η ζ)) → σ)
91, 2, 3, 4, 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: (None)
 Copyright terms: Public domain W3C validator