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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 2505 | . 2 |
3 | eqfnfvd.1 | . . 3 | |
4 | eqfnfvd.2 | . . 3 | |
5 | eqfnfv 5518 | . . 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 2416 wfn 5118 cfv 5123 |
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 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fn 5126 df-fv 5131 |
This theorem is referenced by: foeqcnvco 5691 f1eqcocnv 5692 offeq 5995 tfrlem1 6205 frecrdg 6305 updjudhcoinlf 6965 updjudhcoinrg 6966 seq3val 10231 seqvalcd 10232 seq3feq2 10243 seq3feq 10245 seqfeq3 10285 seq3shft 10610 efcvgfsum 11373 upxp 12441 uptx 12443 dvidlemap 12829 dvrecap 12846 peano4nninf 13200 nninfalllemn 13202 nninfsellemeqinf 13212 nninffeq 13216 refeq 13223 |
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