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Mirrors > Home > NFE Home > Th. List > dveeq2-o | Unicode version |
Description: Quantifier introduction when one pair of variables is distinct. Version of dveeq2 1940 using ax-11o 2141. (Contributed by NM, 2-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dveeq2-o |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1616 |
. 2
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2 | ax-17 1616 |
. 2
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3 | equequ2 1686 |
. 2
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4 | 1, 2, 3 | dvelimf-o 2180 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-4 2135 ax-5o 2136 ax-6o 2137 ax-10o 2139 ax-12o 2142 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: ax11eq 2193 ax11el 2194 ax11inda 2200 ax11v2-o 2201 |
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