Theorem eqsstr3 1531

Description: Substitution of equality into a subclass relationship.

Hypotheses

Ref	Expression
eqsstr3.1	⊢ B = A
eqsstr3.2	⊢ B ⊆ C

Assertion

Ref	Expression
eqsstr3	⊢ A ⊆ C

Proof of Theorem eqsstr3

Step	Hyp	Ref	Expression
1		eqsstr3.1	. . 3 ⊢ B = A
2	1	cleqcomi 1105	. 2 ⊢ A = B
3		eqsstr3.2	. 2 ⊢ B ⊆ C
4	2, 3	eqsstr 1530	1 ⊢ A ⊆ C

Syntax hints:   = wceq 1091   ⊆ wss 1487

This theorem is referenced by:  inss2 1658  dmv 2546  cfom 3710  infmap2 4953  pjoml4 5497  3oa 5558

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-in 1491  df-ss 1492

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