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Theorem syl32anc 1142
 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)
syl32anc.6 (((ψ χ θ) (τ η)) → ζ)
Assertion
Ref Expression
syl32anc (φζ)

Proof of Theorem syl32anc
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 290 . 2 (φ → (τ η))
7 syl32anc.6 . 2 (((ψ χ θ) (τ η)) → ζ)
81, 2, 3, 6, 7syl31anc 1137 1 (φζ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∧ w3a 884 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101 This theorem depends on definitions:  df-bi 110  df-3an 886 This theorem is referenced by:  exple1  8944  leexp2rd  9043
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