Theorem psseq2d 2144

Description: An equality deduction for the proper subclass relationship.

Hypothesis

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

Assertion

Ref	Expression
psseq2d	|- (ph -> (C (. A <-> C (. B))

Proof of Theorem psseq2d

Step	Hyp	Ref	Expression
1		psseq1d.1	. 2 |- (ph -> A = B)
2		psseq2 2139	. 2 |- (A = B -> (C (. A <-> C (. B))
3	1, 2	syl 10	1 |- (ph -> (C (. A <-> C (. B))

Syntax hints:   -> wi 3   <-> wb 146   = wceq 958   (. wpss 2051

This theorem is referenced by:  psseq12d 2145  php3 4521  php3OLD 4522  inf3lem5 4626  infeq5 4630  chpsscon1t 9422  chnlet 9432  atcvatlem 10307  atcvat 10308

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-ne 1590  df-in 2054  df-ss 2056  df-pss 2058

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