Theorem mp3an2 1265

Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994.)

Hypotheses

Ref	Expression
mp3an2.1	⊢ ψ
mp3an2.2	⊢ ((φ ∧ ψ ∧ χ) → θ)

Assertion

Ref	Expression
mp3an2	⊢ ((φ ∧ χ) → θ)

Proof of Theorem mp3an2

Step	Hyp	Ref	Expression
1		mp3an2.1	. 2 ⊢ ψ
2		mp3an2.2	. . 3 ⊢ ((φ ∧ ψ ∧ χ) → θ)
3	2	3expa 1151	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
4	1, 3	mpanl2 662	1 ⊢ ((φ ∧ χ) → θ)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  mp3anl2  1272  oddtfin  4519  vfinncsp  4555