Metamath Proof Explorer


Theorem syl3anc

Description: Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012)

Ref Expression
Hypotheses syl3anc.1 φψ
syl3anc.2 φχ
syl3anc.3 φθ
syl3anc.4 ψχθτ
Assertion syl3anc φτ

Proof

Step Hyp Ref Expression
1 syl3anc.1 φψ
2 syl3anc.2 φχ
3 syl3anc.3 φθ
4 syl3anc.4 ψχθτ
5 1 2 3 3jca φψχθ
6 5 4 syl φτ