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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 2447 |
. 2
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3 | eqfnfvd.1 |
. . 3
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4 | eqfnfvd.2 |
. . 3
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5 | eqfnfv 5413 |
. . 3
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6 | 3, 4, 5 | syl2anc 404 |
. 2
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7 | 2, 6 | mpbird 166 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3965 ax-pow 4017 ax-pr 4047 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-v 2624 df-sbc 2844 df-csb 2937 df-un 3006 df-in 3008 df-ss 3015 df-pw 3437 df-sn 3458 df-pr 3459 df-op 3461 df-uni 3662 df-br 3854 df-opab 3908 df-mpt 3909 df-id 4131 df-xp 4460 df-rel 4461 df-cnv 4462 df-co 4463 df-dm 4464 df-iota 4995 df-fun 5032 df-fn 5033 df-fv 5038 |
This theorem is referenced by: foeqcnvco 5585 f1eqcocnv 5586 tfrlem1 6089 frecrdg 6189 updjudhcoinlf 6827 updjudhcoinrg 6828 iseqvalt 9936 seq3val 9937 iseqoveq 9948 iseqsst 9949 iseqfeq2 9954 seq3feq2 9956 iseqfeq 9959 seq3shft 10335 efcvgfsum 11020 peano4nninf 12199 nninfalllemn 12201 nninfsellemeqinf 12211 |
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