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Theorem 2sb5rf 2195
Description: Reversed double substitution. (Contributed by NM, 3-Feb-2005.) (Revised by Mario Carneiro, 6-Oct-2016.) Remove distinct variable constraints. (Revised by Wolf Lammen, 28-Sep-2018.)
Hypotheses
Ref Expression
2sb5rf.1
2sb5rf.2
Assertion
Ref Expression
2sb5rf
Distinct variable group:   ,

Proof of Theorem 2sb5rf
StepHypRef Expression
1 2sb5rf.2 . . . . 5
2119.41 1971 . . . 4
32exbii 1667 . . 3
4 2sb5rf.1 . . . 4
5419.41 1971 . . 3
63, 5bitri 249 . 2
7 sbequ12r 1993 . . . . 5
8 sbequ12r 1993 . . . . 5
97, 8sylan9bb 699 . . . 4
109pm5.32i 637 . . 3
11102exbii 1668 . 2
12 2ax6e 2194 . . 3
1312biantrur 506 . 2
146, 11, 133bitr4ri 278 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  E.wex 1612  F/wnf 1616  [wsb 1739
This theorem is referenced by:  sbel2x  2203
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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