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Theorem sbequi 2108
 Description: An equality theorem for substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbequi

Proof of Theorem sbequi
StepHypRef Expression
1 hbsb2 2106 . . . . . 6
2 equvini 2040 . . . . . . . 8
3 stdpc7 1938 . . . . . . . . . 10
4 sbequ1 1939 . . . . . . . . . 10
53, 4sylan9 639 . . . . . . . . 9
65eximi 1582 . . . . . . . 8
72, 6syl 16 . . . . . . 7
8 19.35 1607 . . . . . . 7
97, 8sylib 189 . . . . . 6
101, 9sylan9 639 . . . . 5
11 nfsb2 2107 . . . . . 6
121119.9d 1792 . . . . 5
1310, 12syl9 68 . . . 4
1413ex 424 . . 3
1514com23 74 . 2
16 sbequ2 1657 . . . . . 6
1716sps 1766 . . . . 5
1817adantr 452 . . . 4
19 sbequ1 1939 . . . . 5
20 drsb1 2071 . . . . . 6
2120biimprd 215 . . . . 5
2219, 21sylan9r 640 . . . 4
2318, 22syld 42 . . 3
2423ex 424 . 2
25 drsb1 2071 . . . . . 6
2625biimpd 199 . . . . 5
27 stdpc7 1938 . . . . 5
2826, 27sylan9 639 . . . 4
294sps 1766 . . . . 5
3029adantr 452 . . . 4
3128, 30syld 42 . . 3
3231ex 424 . 2
3315, 24, 32pm2.61ii 159 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1546  wex 1547  wsb 1655 This theorem is referenced by:  sbequ  2109 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-6 1740  ax-7 1745  ax-11 1757  ax-12 1946 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656
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