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Theorem opeq2i 3816
Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.)
Hypothesis
Ref Expression
opeq1i.1  |-  A  =  B
Assertion
Ref Expression
opeq2i  |-  <. C ,  A >.  =  <. C ,  B >.

Proof of Theorem opeq2i
StepHypRef Expression
1 opeq1i.1 . 2  |-  A  =  B
2 opeq2 3813 . 2  |-  ( A  =  B  ->  <. C ,  A >.  =  <. C ,  B >. )
31, 2ax-mp 8 1  |-  <. C ,  A >.  =  <. C ,  B >.
Colors of variables: wff set class
Syntax hints:    = wceq 1632   <.cop 3656
This theorem is referenced by:  fnressn  5721  fressnfv  5723  seqomlem1  6478  recmulnq  8604  addresr  8776  seqval  11073  ids1  11453  wrdeqs1cat  11491  ressinbas  13220  oduval  14250  efgi0  15045  efgi1  15046  vrgpinv  15094  frgpnabllem1  15177  zlmval  16486  avril1  20852  ginvsn  21032  nvop  21259  phop  21412  orrvcval4  23680  orrvcoel  23681  orrvccel  23682  vdgr1c  23911  wfrlem14  24340  bnj601  29268  tgrpset  31556  erngset  31611  erngset-rN  31619
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-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662
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