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Theorem equveli 1993
 Description: A variable elimination law for equality with no distinct variable requirements. (Compare equvini 1992.) (Contributed by NM, 1-Mar-2013.) (Proof shortened by Mario Carneiro, 17-Oct-2016.)
Assertion
Ref Expression
equveli

Proof of Theorem equveli
StepHypRef Expression
1 albiim 1611 . 2
2 equequ1 1684 . . . . . . . 8
3 equequ1 1684 . . . . . . . 8
42, 3imbi12d 311 . . . . . . 7
54sps 1755 . . . . . 6
65dral1 1970 . . . . 5
7 equid 1676 . . . . . . 7
8 sp 1748 . . . . . . 7
97, 8mpi 16 . . . . . 6
10 equcomi 1679 . . . . . 6
119, 10syl 15 . . . . 5
126, 11syl6bi 219 . . . 4
14 equequ1 1684 . . . . . . . . . 10
15 equequ1 1684 . . . . . . . . . 10
1614, 15imbi12d 311 . . . . . . . . 9
1716sps 1755 . . . . . . . 8
1817dral2 1971 . . . . . . 7
19 equid 1676 . . . . . . . . . 10
2019a1bi 327 . . . . . . . . 9
2120biimpri 197 . . . . . . . 8
2221sps 1755 . . . . . . 7
2318, 22syl6bi 219 . . . . . 6
2423a1d 22 . . . . 5
25 nfeqf 1963 . . . . . . 7
26 equtr 1682 . . . . . . . . . 10
27 ax-8 1675 . . . . . . . . . 10
2826, 27imim12d 68 . . . . . . . . 9
2919, 28mpii 39 . . . . . . . 8
3029ax-gen 1546 . . . . . . 7
31 spimt 1979 . . . . . . 7
3225, 30, 31sylancl 643 . . . . . 6
3332ex 423 . . . . 5
3424, 33pm2.61i 156 . . . 4