Theorem equsb3 2176

Description: Substitution applied to an atomic wff. (Contributed by Raph Levien and FL, 4-Dec-2005.) Remove dependency on ax-11 1842. (Revised by Wolf Lammen, 21-Sep-2018.)

Assertion

Ref	Expression
equsb3

Distinct variable group:   ,

Proof of Theorem equsb3

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		equsb3lem 2175	. . 3
2	1	sbbii 1746	. 2
3		sbcom3 2153	. . 3
4		nfv 1707	. . . 4
5	4	sbf 2121	. . 3
6	3, 5	bitri 249	. 2
7		equsb3lem 2175	. 2
8	2, 6, 7	3bitr3i 275	1

Syntax hints:  <->wb 184  [wsb 1739

This theorem is referenced by:  sb8eu  2318  sb8euOLD  2319  mo3  2323  sb8iota  5563  mo5f  27383  wl-equsb3  30004  wl-mo3t  30021  wl-sb8eut  30022  sbeqal1  31304  frege55lem1b  37922

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-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740