Theorem 3sstr3g 2091

Description: Substitution of equality into both sides of a subclass relationship.

Hypotheses

Ref	Expression
3sstr3g.1	|- (ph -> A (_ B)
3sstr3g.2	|- A = C
3sstr3g.3	|- B = D

Assertion

Ref	Expression
3sstr3g	|- (ph -> C (_ D)

Proof of Theorem 3sstr3g

Step	Hyp	Ref	Expression
1		3sstr3g.1	. 2 |- (ph -> A (_ B)
2		3sstr3g.2	. . 3 |- A = C
3		3sstr3g.3	. . 3 |- B = D
4	2, 3	sseq12i 2077	. 2 |- (A (_ B <-> C (_ D)
5	1, 4	sylib 198	1 |- (ph -> C (_ D)

Syntax hints:   -> wi 3   = wceq 953   (_ wss 2037

This theorem is referenced by:  bastgt 7564  chsscon3 9299  pjss1co 10002  mdslmd2 10165

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-in 2041  df-ss 2043

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