Theorem psstrd 3714

Description: Proper subclass inclusion is transitive. Deduction form of psstr 3711. (Contributed by David Moews, 1-May-2017.)

Hypotheses

Ref	Expression
psstrd.1	|- ( ph -> A C. B )
psstrd.2	|- ( ph -> B C. C )

Assertion

Ref	Expression
psstrd	|- ( ph -> A C. C )

Proof of Theorem psstrd

Step	Hyp	Ref	Expression
1		psstrd.1	. 2 |- ( ph -> A C. B )
2		psstrd.2	. 2 |- ( ph -> B C. C )
3		psstr 3711	. 2 |- ( ( A C. B /\ B C. C ) -> A C. C )
4	1, 2, 3	syl2anc 693	1 |- ( ph -> A C. C )

Syntax hints:   -> wi 4   C. wpss 3575

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-ne 2795  df-in 3581  df-ss 3588  df-pss 3590

This theorem is referenced by: (None)