Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > f1oeq123d | Unicode version |
Description: Equality deduction for one-to-one onto functions. (Contributed by Mario Carneiro, 27-Jan-2017.) |
Ref | Expression |
---|---|
f1eq123d.1 | |
f1eq123d.2 | |
f1eq123d.3 |
Ref | Expression |
---|---|
f1oeq123d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1eq123d.1 | . . 3 | |
2 | f1oeq1 5431 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | f1eq123d.2 | . . 3 | |
5 | f1oeq2 5432 | . . 3 | |
6 | 4, 5 | syl 14 | . 2 |
7 | f1eq123d.3 | . . 3 | |
8 | f1oeq3 5433 | . . 3 | |
9 | 7, 8 | syl 14 | . 2 |
10 | 3, 6, 9 | 3bitrd 213 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1348 wf1o 5197 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-fun 5200 df-fn 5201 df-f 5202 df-f1 5203 df-fo 5204 df-f1o 5205 |
This theorem is referenced by: f1oprg 5486 ennnfonelemhf1o 12368 |
Copyright terms: Public domain | W3C validator |