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Mirrors > Home > ILE Home > Th. List > eqfnfvd | Unicode version |
Description: Deduction for equality of functions. (Contributed by Mario Carneiro, 24-Jul-2014.) |
Ref | Expression |
---|---|
eqfnfvd.1 |
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eqfnfvd.2 |
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eqfnfvd.3 |
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Ref | Expression |
---|---|
eqfnfvd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqfnfvd.3 |
. . 3
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2 | 1 | ralrimiva 2563 |
. 2
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3 | eqfnfvd.1 |
. . 3
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4 | eqfnfvd.2 |
. . 3
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5 | eqfnfv 5634 |
. . 3
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6 | 3, 4, 5 | syl2anc 411 |
. 2
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7 | 2, 6 | mpbird 167 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-csb 3073 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-iota 5196 df-fun 5237 df-fn 5238 df-fv 5243 |
This theorem is referenced by: foeqcnvco 5812 f1eqcocnv 5813 offeq 6120 tfrlem1 6333 frecrdg 6433 updjudhcoinlf 7109 updjudhcoinrg 7110 nnnninfeq 7156 seq3val 10489 seqvalcd 10490 seq3feq2 10501 seq3feq 10503 seqfeq3 10543 seq3shft 10879 efcvgfsum 11707 xpsfeq 12821 upxp 14229 uptx 14231 dvidlemap 14617 dvrecap 14634 peano4nninf 15214 nninfsellemeqinf 15224 nninffeq 15228 refeq 15235 |
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