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Theorem 1stval2 6093
 Description: Alternate value of the function that extracts the first member of an ordered pair. Definition 5.13 (i) of [Monk1] p. 52. (Contributed by NM, 18-Aug-2006.)
Assertion
Ref Expression
1stval2

Proof of Theorem 1stval2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 elvv 4641 . 2
2 vex 2712 . . . . . 6
3 vex 2712 . . . . . 6
42, 3op1st 6084 . . . . 5
52, 3op1stb 4432 . . . . 5
64, 5eqtr4i 2178 . . . 4
7 fveq2 5461 . . . 4
8 inteq 3806 . . . . 5
98inteqd 3808 . . . 4
106, 7, 93eqtr4a 2213 . . 3
1110exlimivv 1873 . 2
121, 11sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332  wex 1469   wcel 2125  cvv 2709  cop 3559  cint 3803   cxp 4577  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-uni 3769  df-int 3804  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:  1stdm  6120
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