Theorem psseq1i 3696

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

Hypothesis

Ref	Expression
psseq1i.1	|- A = B

Assertion

Ref	Expression
psseq1i	|- ( A C. C <-> B C. C )

Proof of Theorem psseq1i

Step	Hyp	Ref	Expression
1		psseq1i.1	. 2 |- A = B
2		psseq1 3694	. 2 |- ( A = B -> ( A C. C <-> B C. C ) )
3	1, 2	ax-mp 5	1 |- ( A C. C <-> B C. C )

Syntax hints:   <-> wb 196   = wceq 1483   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:  psseq12i  3698