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Mirrors > Home > ILE Home > Th. List > ifeq1d | Unicode version |
Description: Equality deduction for conditional operator. (Contributed by NM, 16-Feb-2005.) |
Ref | Expression |
---|---|
ifeq1d.1 |
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Ref | Expression |
---|---|
ifeq1d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifeq1d.1 |
. 2
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2 | ifeq1 3537 |
. 2
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3 | 1, 2 | syl 14 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rab 2464 df-v 2739 df-un 3133 df-if 3535 |
This theorem is referenced by: ifeq12d 3553 ifbieq1d 3556 ifeq1dadc 3564 iseqf1olemjpcl 10478 iseqf1olemqpcl 10479 iseqf1olemfvp 10480 seq3f1olemqsum 10483 seq3f1olemp 10485 summodc 11372 fsum3 11376 fsum3ser 11386 isumlessdc 11485 prodeq2w 11545 prodmodc 11567 fprodseq 11572 prodssdc 11578 lgsval 14065 |
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