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Mirrors > Home > ILE Home > Th. List > nfcdeq | Unicode version |
Description: If we have a conditional
equality proof, where ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
nfcdeq.1 |
![]() ![]() ![]() ![]() |
nfcdeq.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
nfcdeq |
![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcdeq.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | sbf 1788 |
. 2
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3 | nfv 1539 |
. . 3
![]() ![]() ![]() ![]() | |
4 | nfcdeq.2 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | cdeqri 2963 |
. . 3
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6 | 3, 5 | sbie 1802 |
. 2
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7 | 2, 6 | bitr3i 186 |
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-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-cdeq 2961 |
This theorem is referenced by: nfccdeq 2975 |
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