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Mirrors > Home > ILE Home > Th. List > oveq2i | GIF version |
Description: Equality inference for operation value. (Contributed by NM, 28-Feb-1995.) |
Ref | Expression |
---|---|
oveq1i.1 | ⊢ A = B |
Ref | Expression |
---|---|
oveq2i | ⊢ (𝐶𝐹A) = (𝐶𝐹B) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1i.1 | . 2 ⊢ A = B | |
2 | oveq2 5463 | . 2 ⊢ (A = B → (𝐶𝐹A) = (𝐶𝐹B)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝐶𝐹A) = (𝐶𝐹B) |
Colors of variables: wff set class |
Syntax hints: = wceq 1242 (class class class)co 5455 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-v 2553 df-un 2916 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-br 3756 df-iota 4810 df-fv 4853 df-ov 5458 |
This theorem is referenced by: caov32 5630 oa1suc 5986 nnm1 6033 nnm2 6034 mulidnq 6373 halfnqq 6393 addpinq1 6447 addnqpr1 6543 caucvgprlemm 6639 m1p1sr 6688 m1m1sr 6689 0idsr 6695 1idsr 6696 00sr 6697 pn0sr 6699 mulresr 6735 pitonnlem2 6743 axi2m1 6759 ax1rid 6761 axcnre 6765 add42i 6974 negid 7054 negsub 7055 subneg 7056 negsubdii 7092 apreap 7371 recexaplem2 7415 muleqadd 7431 crap0 7691 2p2e4 7815 3p2e5 7830 3p3e6 7831 4p2e6 7832 4p3e7 7833 4p4e8 7834 5p2e7 7835 5p3e8 7836 5p4e9 7837 5p5e10 7838 6p2e8 7839 6p3e9 7840 6p4e10 7841 7p2e9 7842 7p3e10 7843 8p2e10 7844 3t3e9 7850 8th4div3 7921 halfpm6th 7922 iap0 7925 addltmul 7938 peano2z 8057 nn0n0n1ge2 8087 nneoor 8116 zeo 8119 numsuc 8155 numltc 8163 numsucc 8169 numma 8174 nummul1c 8179 6p5lem 8192 4t3lem 8214 decbin2 8247 fztp 8710 fzprval 8714 fztpval 8715 fzshftral 8740 fz0tp 8751 fzo01 8842 fzo12sn 8843 fzo0to2pr 8844 fzo0to3tp 8845 fzo0to42pr 8846 sqval 8966 cu2 9004 i3 9007 i4 9008 binom2i 9013 binom3 9019 reim0 9089 cji 9130 absi 9223 |
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