Theorem eqimss2 2154

Description: Equality implies the subclass relation.

Assertion

Ref	Expression
eqimss2	|- (B = A -> A (_ B)

Proof of Theorem eqimss2

Step	Hyp	Ref	Expression
1		eqimss 2153	. 2 |- (A = B -> A (_ B)
2	1	eqcoms 1515	1 |- (B = A -> A (_ B)

Syntax hints:   -> wi 3   = wceq 988   (_ wss 2091

This theorem is referenced by:  vss 2352  suc11 3148  dmcoeq 3426  xp11 3532  fconst3 3926  oaass 4279  odi 4294  oen0 4297  zorn 4883  subgres 8236  hstoh 10277  dmdi2 10349

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 994  ax-gen 995  ax-8 996  ax-10 998  ax-12 1000  ax-17 1003  ax-4 1005  ax-5o 1007  ax-6o 1010  ax-9o 1155  ax-10o 1173  ax-16 1243  ax-11o 1251  ax-ext 1494

This theorem depends on definitions:  df-bi 145  df-an 223  df-ex 1013  df-sb 1205  df-clab 1500  df-cleq 1505  df-clel 1508  df-in 2095  df-ss 2097

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