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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 | |
eqfnfvd.2 | |
eqfnfvd.3 |
Ref | Expression |
---|---|
eqfnfvd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqfnfvd.3 | . . 3 | |
2 | 1 | ralrimiva 2503 | . 2 |
3 | eqfnfvd.1 | . . 3 | |
4 | eqfnfvd.2 | . . 3 | |
5 | eqfnfv 5511 | . . 3 | |
6 | 3, 4, 5 | syl2anc 408 | . 2 |
7 | 2, 6 | mpbird 166 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wral 2414 wfn 5113 cfv 5118 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-iota 5083 df-fun 5120 df-fn 5121 df-fv 5126 |
This theorem is referenced by: foeqcnvco 5684 f1eqcocnv 5685 offeq 5988 tfrlem1 6198 frecrdg 6298 updjudhcoinlf 6958 updjudhcoinrg 6959 seq3val 10224 seqvalcd 10225 seq3feq2 10236 seq3feq 10238 seqfeq3 10278 seq3shft 10603 efcvgfsum 11362 upxp 12430 uptx 12432 dvidlemap 12818 dvrecap 12835 peano4nninf 13189 nninfalllemn 13191 nninfsellemeqinf 13201 nninffeq 13205 refeq 13212 |
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