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Theorem ot1stg 6090
 Description: Extract the first member of an ordered triple. (Due to infrequent usage, it isn't worthwhile at this point to define special extractors for triples, so we reuse the ordered pair extractors for ot1stg 6090, ot2ndg 6091, ot3rdgg 6092.) (Contributed by NM, 3-Apr-2015.) (Revised by Mario Carneiro, 2-May-2015.)
Assertion
Ref Expression
ot1stg

Proof of Theorem ot1stg
StepHypRef Expression
1 df-ot 3566 . . . . 5
21fveq2i 5464 . . . 4
3 opexg 4183 . . . . . 6
4 op1stg 6088 . . . . . 6
53, 4sylan 281 . . . . 5
653impa 1177 . . . 4
72, 6syl5eq 2199 . . 3
87fveq2d 5465 . 2
9 op1stg 6088 . . 3
1093adant3 1002 . 2
118, 10eqtrd 2187 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   w3a 963   wceq 1332   wcel 2125  cvv 2709  cop 3559  cotp 3560  cfv 5163  c1st 6076 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-13 2127  ax-14 2128  ax-ext 2136  ax-sep 4078  ax-pow 4130  ax-pr 4164  ax-un 4388 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-eu 2006  df-mo 2007  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-v 2711  df-sbc 2934  df-un 3102  df-in 3104  df-ss 3111  df-pw 3541  df-sn 3562  df-pr 3563  df-op 3565  df-ot 3566  df-uni 3769  df-br 3962  df-opab 4022  df-mpt 4023  df-id 4248  df-xp 4585  df-rel 4586  df-cnv 4587  df-co 4588  df-dm 4589  df-rn 4590  df-iota 5128  df-fun 5165  df-fv 5171  df-1st 6078 This theorem is referenced by: (None)
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