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Theorem syl12anc 1180

Description: Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)

**Assertion**
Ref	Expression
syl12anc

**Proof of Theorem syl12anc**
Step	Hyp	Ref	Expression
1		sylXanc.1	. . 3
2		sylXanc.2	. . 3
3		sylXanc.3	. . 3
4	1, 2, 3	jca32 521	. 2 $/\$ $/\$
5		syl12anc.4	. 2 $/\$ $/\$
6	4, 5	syl 15	1

Colors of variables: wff setvar class

Syntax hints:

wi 4 $/\$ wa 358

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

This theorem is referenced by: syl22anc 1183 raaan 3657 raaanv 3658 nndisjeq 4429 prepeano4 4451 ssfin 4470 ncfinraise 4481 ncfinlower 4483 nnpweq 4523 peano4 4557 f1oiso2 5500 frecsuc 6322