Theorem pm2.43i 43

Description: Inference absorbing redundant antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.)

Hypothesis

Ref	Expression
pm2.43i.1	⊢ (φ → (φ → ψ))

Assertion

Ref	Expression
pm2.43i	⊢ (φ → ψ)

Proof of Theorem pm2.43i

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (φ → φ)
2		pm2.43i.1	. 2 ⊢ (φ → (φ → ψ))
3	1, 2	mpd 14	1 ⊢ (φ → ψ)

Syntax hints:   → wi 4

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

This theorem is referenced by:  sylc  56  pm2.18  102  impbid  183  ibi  232  anidms  626  tbw-bijust  1463  tbw-negdf  1464  equid  1676  equidOLD  1677  hbae  1953  aecom-o  2151  hbae-o  2153  hbequid  2160  equidqe  2173  equid1ALT  2176  ax10from10o  2177  ax11inda  2200  vtoclgaf  2920  vtocl2gaf  2922  vtocl3gaf  2924  elinti  3936  spfinsfincl  4540  copsexg  4608