Theorem expcomd 1452

Description: Deduction form of expcom 116. (Contributed by Alan Sare, 22-Jul-2012.)

Hypothesis

Ref	Expression
expcomd.1	⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))

Assertion

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

Proof of Theorem expcomd

Step	Hyp	Ref	Expression
1		expcomd.1	. . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))
2	1	expd 258	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	com23 78	1 ⊢ (𝜑 → (𝜒 → (𝜓 → 𝜃)))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is referenced by:  simplbi2comg  1454  2moswapdc  2135  indifdir  3420  reupick  3448  issod  4355  poxp  6299  smores2  6361  smoiun  6368  mapxpen  6918  f1dmvrnfibi  7019  recexprlemm  7708  ltleletr  8125  fzind  9458  iccid  10017  ssfzo12bi  10318  dvdsabseq  12029  divalgb  12107  cncongr1  12296  difsqpwdvds  12532  lss1d  14015  txlm  14599  blsscls2  14813  metcnpi3  14837