Theorem a1i13 27

Description: Add two antecedents to a wff. (Contributed by Jeff Hankins, 4-Aug-2009.)

Hypothesis

Ref	Expression
a1i13.1	⊢ (𝜓 → 𝜃)

Assertion

Ref	Expression
a1i13	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Proof of Theorem a1i13

Step	Hyp	Ref	Expression
1		a1i13.1	. . 3 ⊢ (𝜓 → 𝜃)
2	1	a1d 25	. 2 ⊢ (𝜓 → (𝜒 → 𝜃))
3	2	a1i 11	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  propeqop  5512  seqshft2  14069  seqsplit  14076  resqrex  15289  2mulprm  16730  comppfsc  23540  filconn  23891  sinq12ge0  26550  usgr2pth  29784  elwspths2on  29980  frgr3vlem1  30292  3vfriswmgrlem  30296  onsupnmax  43240  cantnfresb  43337  dflim5  43342