Theorem sbcid 3344

Description: An identity theorem for substitution. See sbid 1996. (Contributed by Mario Carneiro, 18-Feb-2017.)

Assertion

Ref	Expression
sbcid

Proof of Theorem sbcid

Step	Hyp	Ref	Expression
1		sbsbc 3331	. 2
2		sbid 1996	. 2
3	1, 2	bitr3i 251	1

Syntax hints:  <->wb 184  [wsb 1739  [.wsbc 3327

This theorem is referenced by:  csbid  3442  snfil  20365  ex-natded9.26  25140  bnj605  33965  elimhyps  34692  dedths  34693

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-12 1854  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-sbc 3328