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Theorem op1std 5717
Description: Extract the first member of an ordered pair. (Contributed by Mario Carneiro, 31-Aug-2015.)
Hypotheses
Ref Expression
op1st.1  _V
op1st.2  _V
Assertion
Ref Expression
op1std  C  <. ,  >.  1st `  C

Proof of Theorem op1std
StepHypRef Expression
1 fveq2 5121 . 2  C  <. ,  >.  1st `  C  1st ` 
<. ,  >.
2 op1st.1 . . 3  _V
3 op1st.2 . . 3  _V
42, 3op1st 5715 . 2  1st `  <. ,  >.
51, 4syl6eq 2085 1  C  <. ,  >.  1st `  C
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   wcel 1390   _Vcvv 2551   <.cop 3370   ` cfv 4845   1stc1st 5707
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935  ax-un 4136
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-sbc 2759  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-opab 3810  df-mpt 3811  df-id 4021  df-xp 4294  df-rel 4295  df-cnv 4296  df-co 4297  df-dm 4298  df-rn 4299  df-iota 4810  df-fun 4847  df-fv 4853  df-1st 5709
This theorem is referenced by:  xp1st  5734  sbcopeq1a  5755  csbopeq1a  5756  eloprabi  5764  mpt2mptsx  5765  dmmpt2ssx  5767  fmpt2x  5768  fmpt2co  5779  df1st2  5782  xporderlem  5793
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