Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1262 Structured version   Unicode version

Theorem bnj1262 32823
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 3547 1  |-  ( ph  ->  C  C_  B )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1374    C_ wss 3469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-in 3476  df-ss 3483
This theorem is referenced by:  bnj229  32896  bnj1128  33000  bnj1145  33003
  Copyright terms: Public domain W3C validator