Theorem mpand 524

Description: A deduction based on modus ponens.

Hypotheses

Ref	Expression
mpand.1	⊢ (φ → ψ)
mpand.2	⊢ (φ → ((ψ ∧ χ) → θ))

Assertion

Ref	Expression
mpand	⊢ (φ → (χ → θ))

Proof of Theorem mpand

Step	Hyp	Ref	Expression
1		mpand.1	. 2 ⊢ (φ → ψ)
2		mpand.2	. . 3 ⊢ (φ → ((ψ ∧ χ) → θ))
3	2	exp3a 292	. 2 ⊢ (φ → (ψ → (χ → θ)))
4	1, 3	mpd 46	1 ⊢ (φ → (χ → θ))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  mp2and 526  orduniorsuc 2337  nnge1t 4439  occllem6 5185  osumlem4 5533  sumdmd 5787

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org