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Theorem bnj1262 29159
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 . . 3  |-  A  C_  B
32a1i 10 . 2  |-  ( ph  ->  A  C_  B )
41, 3eqsstrd 3225 1  |-  ( ph  ->  C  C_  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632    C_ wss 3165
This theorem is referenced by:  bnj229  29232  bnj1128  29336  bnj1145  29339
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-in 3172  df-ss 3179
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