Theorem sseqtr4i 3304

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 4-Apr-1995.)

Hypotheses

Ref	Expression
sseqtr4.1	⊢ A ⊆ B
sseqtr4.2	⊢ C = B

Assertion

Ref	Expression
sseqtr4i	⊢ A ⊆ C

Proof of Theorem sseqtr4i

Step	Hyp	Ref	Expression
1		sseqtr4.1	. 2 ⊢ A ⊆ B
2		sseqtr4.2	. . 3 ⊢ C = B
3	2	eqcomi 2357	. 2 ⊢ B = C
4	1, 3	sseqtri 3303	1 ⊢ A ⊆ C

Syntax hints:   = wceq 1642   ⊆ wss 3257

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  eqimss2i  3326  snsspr1  3856  snsspr2  3857  snsstp1  3858  snsstp2  3859  snsstp3  3860  unissint  3950  iunxdif2  4014  snprss1  4120  opabssxp  4837  dmresi  5004  cnvimass  5016  ssrnres  5059  fvfullfunlem3  5863  mapsspm  6021  sbthlem1  6203