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Theorem sseqtr4d 3308
 Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
sseqtr4d.1 (φA B)
sseqtr4d.2 (φC = B)
Assertion
Ref Expression
sseqtr4d (φA C)

Proof of Theorem sseqtr4d
StepHypRef Expression
1 sseqtr4d.1 . 2 (φA B)
2 sseqtr4d.2 . . 3 (φC = B)
32eqcomd 2358 . 2 (φB = C)
41, 3sseqtrd 3307 1 (φA C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ⊆ wss 3257 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-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  syl5sseqr  3320  sbthlem1  6203  sbthlem3  6205
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