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Mirrors > Home > ILE Home > Th. List > equs5 | Unicode version |
Description: Lemma used in proofs of substitution properties. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
equs5 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbnae 1721 |
. 2
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2 | hba1 1540 |
. 2
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3 | ax11o 1822 |
. . 3
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4 | 3 | impd 254 |
. 2
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5 | 1, 2, 4 | exlimdh 1596 |
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-in1 614 ax-in2 615 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-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 |
This theorem is referenced by: sb3 1831 sb4 1832 |
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