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Theorem ghgrplem2OLD 25583
 Description: Obsolete as of 14-Mar-2020. Lemma for ghgrpOLD 25584. (Contributed by Paul Chapman, 25-Apr-2008.) (Revised by Mario Carneiro, 12-May-2014.) (New usage is discouraged.)
Hypotheses
Ref Expression
ghgrpOLD.1
ghgrpOLD.2
ghgrpOLD.3
Assertion
Ref Expression
ghgrplem2OLD
Distinct variable groups:   ,,   ,,   ,,   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem ghgrplem2OLD
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ghgrpOLD.2 . . . . 5
21ralrimivva 2878 . . . 4
3 oveq1 6303 . . . . . . 7
43fveq2d 5876 . . . . . 6
5 fveq2 5872 . . . . . . 7
65oveq1d 6311 . . . . . 6
74, 6eqeq12d 2479 . . . . 5
8 oveq2 6304 . . . . . . 7
98fveq2d 5876 . . . . . 6
10 fveq2 5872 . . . . . . 7
1110oveq2d 6312 . . . . . 6
129, 11eqeq12d 2479 . . . . 5
137, 12cbvral2v 3092 . . . 4
142, 13sylib 196 . . 3
15 oveq1 6303 . . . . . 6
1615fveq2d 5876 . . . . 5
17 fveq2 5872 . . . . . 6
1817oveq1d 6311 . . . . 5
1916, 18eqeq12d 2479 . . . 4
20 oveq2 6304 . . . . . 6
2120fveq2d 5876 . . . . 5
22 fveq2 5872 . . . . . 6
2322oveq2d 6312 . . . . 5
2421, 23eqeq12d 2479 . . . 4
2519, 24rspc2v 3219 . . 3
2614, 25mpan9 469 . 2
27 ghgrpOLD.3 . . . 4
2827oveqi 6309 . . 3
29 ghgrpOLD.1 . . . . . 6
30 fof 5801 . . . . . 6
3129, 30syl 16 . . . . 5
32 ffvelrn 6030 . . . . . 6
33 ffvelrn 6030 . . . . . 6
3432, 33anim12dan 837 . . . . 5
3531, 34sylan 471 . . . 4
36 ovres 6441 . . . 4
3735, 36syl 16 . . 3
3828, 37syl5eq 2510 . 2
3926, 38eqtr4d 2501 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1395   wcel 1819  wral 2807   cxp 5006   cres 5010  wf 5590  wfo 5592  cfv 5594  (class class class)co 6296 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  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 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-opab 4516  df-id 4804  df-xp 5014  df-rel 5015  df-cnv 5016  df-co 5017  df-dm 5018  df-rn 5019  df-res 5020  df-iota 5557  df-fun 5596  df-fn 5597  df-f 5598  df-fo 5600  df-fv 5602  df-ov 6299 This theorem is referenced by:  ghgrpOLD  25584  ghabloOLD  25585
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