Theorem csbtt 3445

Description: Substitution doesn't affect a constant (in which is not free). (Contributed by Mario Carneiro, 14-Oct-2016.)

Assertion

Ref	Expression
csbtt

Proof of Theorem csbtt

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-csb 3435	. 2
2		nfcr 2610	. . . 4
3		sbctt 3398	. . . 4
4	2, 3	sylan2 474	. . 3
5	4	abbi1dv 2595	. 2
6	1, 5	syl5eq 2510	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  e.wcel 1818  {cab 2442  F/_wnfc 2605  [.wsbc 3327  [_csb 3434

This theorem is referenced by:  csbconstgf  3446  sbnfc2  3854  constlimc  31630

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  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435