Theorem mpd3an3 1278

Description: An inference based on modus ponens. (Contributed by NM, 8-Nov-2007.)

Hypotheses

Ref	Expression
mpd3an3.2	⊢ ((φ ∧ ψ) → χ)
mpd3an3.3	⊢ ((φ ∧ ψ ∧ χ) → θ)

Assertion

Ref	Expression
mpd3an3	⊢ ((φ ∧ ψ) → θ)

Proof of Theorem mpd3an3

Step	Hyp	Ref	Expression
1		mpd3an3.2	. 2 ⊢ ((φ ∧ ψ) → χ)
2		mpd3an3.3	. . 3 ⊢ ((φ ∧ ψ ∧ χ) → θ)
3	2	3expa 1151	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
4	1, 3	mpdan 649	1 ⊢ ((φ ∧ ψ) → 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:  nnsucelr  4429  cupvalg  5813  ovcross  5846  pmvalg  6011  enadj  6061  ovmuc  6131  ovce  6173  addlecncs  6210  leconnnc  6219  ncslesuc  6268