Theorem expdcom 1383

Description: Commuted form of expd 255. (Contributed by Alan Sare, 18-Mar-2012.)

Hypothesis

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

Assertion

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

Proof of Theorem expdcom

Step	Hyp	Ref	Expression
1		expdcom.1	. . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))
2	1	expd 255	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	com3l 81	1 ⊢ (𝜓 → (𝜒 → (𝜑 → 𝜃)))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 107

This theorem is referenced by:  nndi  6287  nnmass  6288  mulexp  10125  expadd  10128  expmul  10131