Theorem mp3anr2 1487

Description: An inference based on modus ponens. (Contributed by NM, 24-Nov-2006.)

Hypotheses

Ref	Expression
mp3anr2.1	⊢ 𝜒
mp3anr2.2	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜏)

Assertion

Ref	Expression
mp3anr2	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜃)) → 𝜏)

Proof of Theorem mp3anr2

Step	Hyp	Ref	Expression
1		mp3anr2.1	. . 3 ⊢ 𝜒
2		mp3anr2.2	. . . 4 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜏)
3	2	ancoms 463	. . 3 ⊢ (((𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜑) → 𝜏)
4	1, 3	mp3anl2 1484	. 2 ⊢ (((𝜓 ∧ 𝜃) ∧ 𝜑) → 𝜏)
5	4	ancoms 463	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜃)) → 𝜏)

This proof depends on syntax axioms:   → wi 4   ∧ wa 400   ∧ w3a 1102

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-3an 1104

This theorem is used by:  mulgp1  19179  vcz  30938  nvmdi  31011