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Theorem xpexgALT 6777
 Description: Alternate proof of xpexg 6710 requiring Replacement (ax-rep 4558) but not Power Set (ax-pow 4625). (Contributed by Mario Carneiro, 20-May-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
xpexgALT

Proof of Theorem xpexgALT
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 iunid 4380 . . . 4
21xpeq2i 5020 . . 3
3 xpiundi 5053 . . 3
42, 3eqtr3i 2498 . 2
5 id 22 . . 3
6 fconstmpt 5042 . . . . 5
7 mptexg 6129 . . . . 5
86, 7syl5eqel 2559 . . . 4
98ralrimivw 2879 . . 3
10 iunexg 6760 . . 3
115, 9, 10syl2anr 478 . 2
124, 11syl5eqel 2559 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wcel 1767  wral 2814  cvv 3113  csn 4027  ciun 4325   cmpt 4505   cxp 4997 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-rep 4558  ax-sep 4568  ax-nul 4576  ax-pr 4686  ax-un 6575 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-reu 2821  df-rab 2823  df-v 3115  df-sbc 3332  df-csb 3436  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-iun 4327  df-br 4448  df-opab 4506  df-mpt 4507  df-id 4795  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-rn 5010  df-res 5011  df-ima 5012  df-iota 5550  df-fun 5589  df-fn 5590  df-f 5591  df-f1 5592  df-fo 5593  df-f1o 5594  df-fv 5595 This theorem is referenced by: (None)
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