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Theorem sb5ALT 28546
 Description: Equivalence for substitution. Alternate proof of sb5 2175. This proof is sb5ALTVD 28962 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sb5ALT
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem sb5ALT
StepHypRef Expression
1 equsb1 2113 . . . 4
2 sban 2143 . . . . 5
32simplbi2com 1383 . . . 4
41, 3mpi 17 . . 3
5 spsbe 1663 . . 3
64, 5syl 16 . 2
7 hbs1 2180 . . 3
8 simpr 448 . . . . 5
98a1i 11 . . . 4
10 simpl 444 . . . . 5
1110a1i 11 . . . 4
12 sbequ1 1943 . . . . 5
1312com12 29 . . . 4
149, 11, 13ee22 1371 . . 3
157, 14exlimexi 28545 . 2
166, 15impbii 181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wsb 1658 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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