Yes, it does. That just basic math. a/c=a/d=b/c=b/d pretty obviously shows a transitive relation! How can you possibly deny this? (Try this, given A=B=C=D, then, by necessity, A=C, A=D, B=A, and B=C. As A=B and B=C so must A=C or A=C and C=D so must A=D, etc. Really simple stuff here. Well, unless you're an autodidact -- those guys have a lot of trouble with stuff like this.)
If you actually want to continue making "your" ridiculous claim, in face of evidence that makes it look foolish, you'll need to show me a case where PHP's == operator is intransitive without mixing types.
Betcha can't do that!