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Mirrors > Home > MPE Home > Th. List > inteqi | Structured version Visualization version GIF version |
Description: Equality inference for class intersection. (Contributed by NM, 2-Sep-2003.) |
Ref | Expression |
---|---|
inteqi.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
inteqi | ⊢ ∩ 𝐴 = ∩ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inteqi.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | inteq 4953 | . 2 ⊢ (𝐴 = 𝐵 → ∩ 𝐴 = ∩ 𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∩ 𝐴 = ∩ 𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 ∩ cint 4950 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-ral 3059 df-rex 3068 df-int 4951 |
This theorem is referenced by: elintrab 4964 ssintrab 4975 intmin2 4979 intsng 4987 intexrab 5352 intabs 5354 op1stb 5481 dfiin3g 5981 op2ndb 6248 ordintdif 6435 knatar 7376 uniordint 7820 oawordeulem 8590 oeeulem 8637 naddov3 8716 iinfi 9454 dfttrcl2 9761 tcsni 9780 rankval2 9855 rankval3b 9863 cf0 10288 cfval2 10297 cofsmo 10306 isf34lem4 10414 isf34lem7 10416 sstskm 10879 dfnn3 12277 trclun 15049 cycsubg 19238 efgval2 19756 00lsp 20996 alexsublem 24067 noextendlt 27728 nosepne 27739 nosepdm 27743 nosupbnd2lem1 27774 noinfbnd2lem1 27789 noetasuplem4 27795 bday0s 27887 intimafv 32725 dynkin 34147 imaiinfv 42680 elrfi 42681 onuniintrab 43214 naddov4 43372 naddwordnexlem4 43390 harval3 43527 relintab 43572 dfid7 43601 clcnvlem 43612 dfrtrcl5 43618 dfrcl2 43663 aiotajust 47033 dfaiota2 47035 ipolub0 48780 |
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