Theorem sbhypf 3156

Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf 3453. (Contributed by Raph Levien, 10-Apr-2004.)

Hypotheses

Ref	Expression
sbhypf.1
sbhypf.2

Assertion

Ref	Expression
sbhypf

Distinct variable groups:   ,   ,

Proof of Theorem sbhypf

Step	Hyp	Ref	Expression
1		vex 3112	. . 3
2		eqeq1 2461	. . 3
3	1, 2	ceqsexv 3146	. 2
4		nfs1v 2181	. . . 4
5		sbhypf.1	. . . 4
6	4, 5	nfbi 1934	. . 3
7		sbequ12 1992	. . . . 5
8	7	bicomd 201	. . . 4
9		sbhypf.2	. . . 4
10	8, 9	sylan9bb 699	. . 3
11	6, 10	exlimi 1912	. 2
12	3, 11	sylbir 213	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  [wsb 1739

This theorem is referenced by:  mob2  3279  reu2eqd  3296  ralxpf  5154  tfisi  6693  ac6sf  8890  nn0ind-raph  10989  cbvmptf  27494  nn0min  27611  ac6gf  30223  fdc1  30239

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  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-v 3111