Theorem psseq12i 3035

Description: An equality inference for the proper subclass relationship. (Contributed by NM, 9-Jun-2004.)

Hypotheses

Ref	Expression
psseq1i.1	|- A = B
psseq12i.2	|- C = D

Assertion

Ref	Expression
psseq12i	|- ( A C. C <-> B C. D )

Proof of Theorem psseq12i

Step	Hyp	Ref	Expression
1		psseq1i.1	. . 3 |- A = B
2	1	psseq1i 3033	. 2 |- ( A C. C <-> B C. C )
3		psseq12i.2	. . 3 |- C = D
4	3	psseq2i 3034	. 2 |- ( B C. C <-> B C. D )
5	2, 4	bitri 173	1 |- ( A C. C <-> B C. D )

Syntax hints:   <-> wb 98   = wceq 1243   C. wpss 2918

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ne 2206  df-in 2924  df-ss 2931  df-pss 2933

This theorem is referenced by: (None)