Theorem psseq1d 3036

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

Hypothesis

Ref	Expression
psseq1d.1	|- ( ph -> A = B )

Assertion

Ref	Expression
psseq1d	|- ( ph -> ( A C. C <-> B C. C ) )

Proof of Theorem psseq1d

Step	Hyp	Ref	Expression
1		psseq1d.1	. 2 |- ( ph -> A = B )
2		psseq1 3031	. 2 |- ( A = B -> ( A C. C <-> B C. C ) )
3	1, 2	syl 14	1 |- ( ph -> ( A C. C <-> B C. C ) )

Syntax hints:   -> wi 4   <-> 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:  psseq12d  3038