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Mirrors > Home > MPE Home > Th. List > sbequ1 | Unicode version |
Description: An equality theorem for substitution. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sbequ1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.4 545 |
. . 3
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2 | 19.8a 1758 |
. . 3
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3 | df-sb 1656 |
. . 3
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4 | 1, 2, 3 | sylanbrc 646 |
. 2
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5 | 4 | ex 424 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem is referenced by: sbequ12 1940 dfsb2 2104 sbequi 2108 sbn 2111 sbi1 2112 sb6rf 2140 mo 2276 sb5ALT 28320 2pm13.193 28350 2pm13.193VD 28724 sb5ALTVD 28734 sbnNEW7 29266 sbi1NEW7 29267 sbequiNEW7 29282 sb6rfNEW7 29293 dfsb2NEW7 29339 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-11 1757 |
This theorem depends on definitions: df-bi 178 df-an 361 df-ex 1548 df-sb 1656 |
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