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Mirrors > Home > NFE Home > Th. List > nfiso | Unicode version |
Description: Bound-variable hypothesis builder for an isomorphism. (Contributed by NM, 17-May-2004.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
nfiso.1 |
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nfiso.2 |
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nfiso.3 |
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nfiso.4 |
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nfiso.5 |
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Ref | Expression |
---|---|
nfiso |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iso 4796 |
. 2
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2 | nfiso.1 |
. . . 4
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3 | nfiso.4 |
. . . 4
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4 | nfiso.5 |
. . . 4
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5 | 2, 3, 4 | nff1o 5285 |
. . 3
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6 | nfcv 2489 |
. . . . . . 7
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7 | nfiso.2 |
. . . . . . 7
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8 | nfcv 2489 |
. . . . . . 7
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9 | 6, 7, 8 | nfbr 4683 |
. . . . . 6
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10 | 2, 6 | nffv 5334 |
. . . . . . 7
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11 | nfiso.3 |
. . . . . . 7
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12 | 2, 8 | nffv 5334 |
. . . . . . 7
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13 | 10, 11, 12 | nfbr 4683 |
. . . . . 6
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14 | 9, 13 | nfbi 1834 |
. . . . 5
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15 | 3, 14 | nfral 2667 |
. . . 4
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16 | 3, 15 | nfral 2667 |
. . 3
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17 | 5, 16 | nfan 1824 |
. 2
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18 | 1, 17 | nfxfr 1570 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-xp 4079 ax-cnv 4080 ax-1c 4081 ax-sset 4082 ax-si 4083 ax-ins2 4084 ax-ins3 4085 ax-typlower 4086 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-symdif 3216 df-ss 3259 df-nul 3551 df-if 3663 df-pw 3724 df-sn 3741 df-pr 3742 df-uni 3892 df-int 3927 df-opk 4058 df-1c 4136 df-pw1 4137 df-uni1 4138 df-xpk 4185 df-cnvk 4186 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-cok 4190 df-p6 4191 df-sik 4192 df-ssetk 4193 df-imagek 4194 df-idk 4195 df-iota 4339 df-addc 4378 df-nnc 4379 df-phi 4565 df-op 4566 df-opab 4623 df-br 4640 df-co 4726 df-ima 4727 df-cnv 4785 df-rn 4786 df-dm 4787 df-fun 4789 df-fn 4790 df-f 4791 df-f1 4792 df-fo 4793 df-f1o 4794 df-fv 4795 df-iso 4796 |
This theorem is referenced by: (None) |
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