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Theorem ixpssmap2g 7518
Description: An infinite Cartesian product is a subset of set exponentiation. This version of ixpssmapg 7519 avoids ax-rep 4563. (Contributed by Mario Carneiro, 16-Nov-2014.)
Assertion
Ref Expression
ixpssmap2g
Distinct variable group:   ,

Proof of Theorem ixpssmap2g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ixpf 7511 . . . . 5
21adantl 466 . . . 4
3 n0i 3789 . . . . . 6
4 ixpprc 7510 . . . . . 6
53, 4nsyl2 127 . . . . 5
6 elmapg 7452 . . . . 5
75, 6sylan2 474 . . . 4
82, 7mpbird 232 . . 3
98ex 434 . 2
109ssrdv 3509 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818   cvv 3109  C_wss 3475   c0 3784  U_ciun 4330  -->wf 5589  (class class class)co 6296   cmap 7439  X_cixp 7489
This theorem is referenced by:  ixpssmapg  7519  ixpfi  7837  ixpiunwdom  8038  prdsval  14852  prdsbas  14854
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pow 4630  ax-pr 4691  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-pw 4014  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-map 7441  df-ixp 7490
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