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Theorem efgmval 16526
 Description: Value of the formal inverse operation for the generating set of a free group. (Contributed by Mario Carneiro, 27-Sep-2015.)
Hypothesis
Ref Expression
efgmval.m
Assertion
Ref Expression
efgmval
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem efgmval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 opeq1 4213 . 2
2 difeq2 3616 . . 3
32opeq2d 4220 . 2
4 efgmval.m . . 3
5 opeq1 4213 . . . 4
6 difeq2 3616 . . . . 5
76opeq2d 4220 . . . 4
85, 7cbvmpt2v 6359 . . 3
94, 8eqtri 2496 . 2
10 opex 4711 . 2
111, 3, 9, 10ovmpt2 6420 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1379   wcel 1767   cdif 3473  cop 4033  (class class class)co 6282   cmpt2 6284  c1o 7120  c2o 7121 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-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686 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-rab 2823  df-v 3115  df-sbc 3332  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-br 4448  df-opab 4506  df-id 4795  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-iota 5549  df-fun 5588  df-fv 5594  df-ov 6285  df-oprab 6286  df-mpt2 6287 This theorem is referenced by:  efgmnvl  16528  efgval2  16538  vrgpinv  16583  frgpuptinv  16585  frgpuplem  16586  frgpnabllem1  16668
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