Theorem 2a1i 27

Description: Add two antecedents to a wff. (Contributed by Jeff Hankins, 4-Aug-2009.) (Proof shortened by Wolf Lammen, 23-Jul-2013.)

Hypothesis

Ref	Expression
2a1i.1	|- ch

Assertion

Ref	Expression
2a1i	|- ( ph -> ( ps -> ch ) )

Proof of Theorem 2a1i

Step	Hyp	Ref	Expression
1		2a1i.1	. . 3 |- ch
2	1	a1i 9	. 2 |- ( ph -> ch )
3	2	a1d 22	1 |- ( ph -> ( ps -> ch ) )

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  equvini  1811  sbcrext  3129  map1  7101  modom  7108  seq3id2  10963  pfxccatin12lem3  11504  fsum2d  12202  fsumabs  12232  fsumiun  12244  fprod2d  12390  cncfmptc  15697