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Mirrors > Home > ILE Home > Th. List > eqcomi | Unicode version |
Description: Inference from commutative law for class equality. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqcomi.1 |
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Ref | Expression |
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eqcomi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcomi.1 |
. 2
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2 | eqcom 2142 |
. 2
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3 | 1, 2 | mpbi 144 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 |
This theorem is referenced by: eqtr2i 2162 eqtr3i 2163 eqtr4i 2164 syl5eqr 2187 syl5reqr 2188 eqtr4di 2191 eqtr4id 2192 eqeltrri 2214 eleqtrri 2216 eqeltrrid 2228 eleqtrrdi 2234 abid2 2261 abid2f 2307 eqnetrri 2334 neeqtrri 2338 eqsstrri 3135 sseqtrri 3137 eqsstrrid 3149 sseqtrrdi 3151 difdif2ss 3338 inrab2 3354 dfopg 3711 opid 3731 eqbrtrri 3959 breqtrri 3963 breqtrrdi 3978 pwin 4212 limon 4437 tfis 4505 dfdm2 5081 cnvresid 5205 fores 5362 funcoeqres 5406 f1oprg 5419 fmptpr 5620 fsnunres 5630 riotaprop 5761 fo1st 6063 fo2nd 6064 fnmpoovd 6120 ixpsnf1o 6638 phplem4 6757 snnen2og 6761 phplem4on 6769 sbthlemi5 6857 eldju 6961 casefun 6978 omp1eomlem 6987 exmidfodomrlemim 7074 caucvgsrlembound 7626 ax0id 7710 1p1e2 8861 1e2m1 8863 2p1e3 8877 3p1e4 8879 4p1e5 8880 5p1e6 8881 6p1e7 8882 7p1e8 8883 8p1e9 8884 div4p1lem1div2 8997 0mnnnnn0 9033 zeo 9180 num0u 9216 numsucc 9245 decsucc 9246 1e0p1 9247 nummac 9250 decsubi 9268 decmul1 9269 decmul10add 9274 6p5lem 9275 10m1e9 9301 5t5e25 9308 6t6e36 9313 8t6e48 9324 decbin3 9347 infrenegsupex 9416 ige3m2fz 9860 fseq1p1m1 9905 fz0tp 9932 1fv 9947 fzo0to42pr 10028 fzosplitprm1 10042 expnegap0 10332 sq4e2t8 10421 3dec 10492 fihashen1 10577 pr0hash2ex 10593 imi 10704 infxrnegsupex 11064 zsumdc 11185 fsumadd 11207 hashrabrex 11282 ntrivcvgap 11349 efsep 11434 3dvdsdec 11598 3dvds2dec 11599 flodddiv4 11667 lcmneg 11791 ennnfonelem1 11956 ndxid 12022 2strstr1g 12101 toponrestid 12227 istpsi 12245 distopon 12295 distps 12299 discld 12344 txbas 12466 txdis 12485 txdis1cn 12486 txhmeo 12527 txswaphmeolem 12528 dvexp 12883 sinq34lt0t 12960 loge 12996 2logb9irr 13096 2logb9irrALT 13099 sqrt2cxp2logb9e3 13100 2logb9irrap 13102 ex-ceil 13109 ex-gcd 13114 bdceqir 13213 bj-ssom 13305 trilpolemgt1 13407 redcwlpolemeq1 13421 |
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