Users' Mathboxes Mathbox for Frédéric Liné < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  difeq12dOLD Unicode version

Theorem difeq12dOLD 24967
Description: Deduction adding difference to the right in a class equality. (Moved into main set.mm as difeq12d 3295 and may be deleted by mathbox owner, FL. --NM 2-Jul-2014.) (Contributed by FL, 29-May-2014.)
Hypotheses
Ref Expression
difeq12dOLD.1  |-  ( ph  ->  A  =  B )
difeq12dOLD.2  |-  ( ph  ->  C  =  D )
Assertion
Ref Expression
difeq12dOLD  |-  ( ph  ->  ( A  \  C
)  =  ( B 
\  D ) )

Proof of Theorem difeq12dOLD
StepHypRef Expression
1 difeq12dOLD.1 . 2  |-  ( ph  ->  A  =  B )
2 difeq12dOLD.2 . 2  |-  ( ph  ->  C  =  D )
31, 2difeq12d 3295 1  |-  ( ph  ->  ( A  \  C
)  =  ( B 
\  D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    \ cdif 3149
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rab 2552  df-dif 3155
  Copyright terms: Public domain W3C validator