Theorem eqsstr3i 2970

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 19-Oct-1999.)

Hypotheses

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

Assertion

Ref	Expression
eqsstr3i	⊢ A ⊆ 𝐶

Proof of Theorem eqsstr3i

Step	Hyp	Ref	Expression
1		eqsstr3.1	. . 3 ⊢ B = A
2	1	eqcomi 2041	. 2 ⊢ A = B
3		eqsstr3.2	. 2 ⊢ B ⊆ 𝐶
4	2, 3	eqsstri 2969	1 ⊢ A ⊆ 𝐶

Syntax hints:   = wceq 1242   ⊆ wss 2911

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925

This theorem is referenced by:  inss2  3152  dmv  4494  resasplitss  5012  ofrfval  5662  fnofval  5663  ofrval  5664  off  5666  ofres  5667  ofco  5671  dftpos4  5819  smores2  5850