Theorem 2sb6rf 2196

Description: Reversed double substitution. (Contributed by NM, 3-Feb-2005.) (Revised by Mario Carneiro, 6-Oct-2016.) Remove variable constraints. (Revised by Wolf Lammen, 28-Sep-2018.)

Hypotheses

Ref	Expression
2sb5rf.1
2sb5rf.2

Assertion

Ref	Expression
2sb6rf

Distinct variable group:   ,

Proof of Theorem 2sb6rf

Step	Hyp	Ref	Expression
1		sbequ12r 1993	. . . . 5
2		sbequ12r 1993	. . . . 5
3	1, 2	sylan9bb 699	. . . 4
4	3	pm5.74i 245	. . 3
5	4	2albii 1641	. 2
6		2sb5rf.2	. . . . 5
7	6	19.23 1910	. . . 4
8	7	albii 1640	. . 3
9		2sb5rf.1	. . . 4
10	9	19.23 1910	. . 3
11	8, 10	bitri 249	. 2
12		2ax6e 2194	. . 3
13		pm5.5 336	. . 3
14	12, 13	ax-mp 5	. 2
15	5, 11, 14	3bitrri 272	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616  [wsb 1739

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