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Theorem sseqtrd 3307
 Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
sseqtrd.1 (φA B)
sseqtrd.2 (φB = C)
Assertion
Ref Expression
sseqtrd (φA C)

Proof of Theorem sseqtrd
StepHypRef Expression
1 sseqtrd.1 . 2 (φA B)
2 sseqtrd.2 . . 3 (φB = C)
32sseq2d 3299 . 2 (φ → (A BA C))
41, 3mpbid 201 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:  sseqtr4d  3308  uniintsn  3963  lenc  6223
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