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Theorem psseq1d 3361
 Description: An equality deduction for the proper subclass relationship. (Contributed by NM, 9-Jun-2004.)
Hypothesis
Ref Expression
psseq1d.1 (φA = B)
Assertion
Ref Expression
psseq1d (φ → (ACBC))

Proof of Theorem psseq1d
StepHypRef Expression
1 psseq1d.1 . 2 (φA = B)
2 psseq1 3356 . 2 (A = B → (ACBC))
31, 2syl 15 1 (φ → (ACBC))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ⊊ wpss 3258 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pss 3261 This theorem is referenced by:  psseq12d  3363
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