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Theorem bnj1262 28513
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1262.1  |-  A  C_  B
bnj1262.2  |-  ( ph  ->  C  =  A )
Assertion
Ref Expression
bnj1262  |-  ( ph  ->  C  C_  B )

Proof of Theorem bnj1262
StepHypRef Expression
1 bnj1262.2 . 2  |-  ( ph  ->  C  =  A )
2 bnj1262.1 . 2  |-  A  C_  B
31, 2syl6eqss 3334 1  |-  ( ph  ->  C  C_  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    C_ wss 3256
This theorem is referenced by:  bnj229  28586  bnj1128  28690  bnj1145  28693
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-in 3263  df-ss 3270
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