Theorem sbcom4 2190

Description: Commutativity law for substitution. This theorem was incorrectly used as our previous version of pm11.07 2191 but may still be useful. (Contributed by Andrew Salmon, 17-Jun-2011.) (Proof shortened by Jim Kingdon, 22-Jan-2018.)

Assertion

Ref	Expression
sbcom4

Distinct variable groups:   ,,,   ,,

Proof of Theorem sbcom4

Step	Hyp	Ref	Expression
1		nfv 1707	. . 3
2	1	sbf 2121	. 2
3		nfv 1707	. . . 4
4	3	sbf 2121	. . 3
5	4	sbbii 1746	. 2
6	3	sbf 2121	. . . 4
7	6	sbbii 1746	. . 3
8	1	sbf 2121	. . 3
9	7, 8	bitri 249	. 2
10	2, 5, 9	3bitr4i 277	1

Syntax hints:  <->wb 184  [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-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