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Mirrors > Home > ILE Home > Th. List > ax-7 | Unicode version |
Description: Axiom of Quantifier Commutation. This axiom says universal quantifiers can be swapped. One of the predicate logic axioms which do not involve equality. Axiom scheme C6' in [Megill] p. 448 (p. 16 of the preprint). Also appears as Lemma 12 of [Monk2] p. 109 and Axiom C5-3 of [Monk2] p. 113. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
ax-7 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph |
. . . 4
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2 | vy |
. . . 4
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3 | 1, 2 | wal 1294 |
. . 3
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4 | vx |
. . 3
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5 | 3, 4 | wal 1294 |
. 2
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6 | 1, 4 | wal 1294 |
. . 3
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7 | 6, 2 | wal 1294 |
. 2
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8 | 5, 7 | wi 4 |
1
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Colors of variables: wff set class |
This axiom is referenced by: a7s 1395 alcoms 1417 hbal 1418 alcom 1419 hbald 1432 hbae 1660 bj-hbalt 12376 |
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