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Mirrors > Home > ILE Home > Th. List > r19.43 | Unicode version |
Description: Restricted version of Theorem 19.43 of [Margaris] p. 90. (Contributed by NM, 27-May-1998.) (Proof rewritten by Jim Kingdon, 5-Jun-2018.) |
Ref | Expression |
---|---|
r19.43 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2461 |
. . . 4
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2 | andi 818 |
. . . . 5
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3 | 2 | exbii 1605 |
. . . 4
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4 | 1, 3 | bitri 184 |
. . 3
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5 | 19.43 1628 |
. . 3
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6 | 4, 5 | bitri 184 |
. 2
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7 | df-rex 2461 |
. . 3
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8 | df-rex 2461 |
. . 3
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9 | 7, 8 | orbi12i 764 |
. 2
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10 | 6, 9 | bitr4i 187 |
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-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-rex 2461 |
This theorem is referenced by: r19.44av 2636 r19.45av 2637 r19.45mv 3516 r19.44mv 3517 iunun 3962 ltexprlemloc 7594 pythagtriplem2 12246 pythagtrip 12263 |
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