Theorem orim12d 811

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 10-May-1994.)

Hypotheses

Ref	Expression
orim12d.1	⊢ (φ → (ψ → χ))
orim12d.2	⊢ (φ → (θ → τ))

Assertion

Ref	Expression
orim12d	⊢ (φ → ((ψ ∨ θ) → (χ ∨ τ)))

Proof of Theorem orim12d

Step	Hyp	Ref	Expression
1		orim12d.1	. 2 ⊢ (φ → (ψ → χ))
2		orim12d.2	. 2 ⊢ (φ → (θ → τ))
3		pm3.48 806	. 2 ⊢ (((ψ → χ) ∧ (θ → τ)) → ((ψ ∨ θ) → (χ ∨ τ)))
4	1, 2, 3	syl2anc 642	1 ⊢ (φ → ((ψ ∨ θ) → (χ ∨ τ)))

Syntax hints:   → wi 4   ∨ wo 357

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-or 359  df-an 360

This theorem is referenced by:  orim1d  812  orim2d  813  3orim123d  1260  preq12b  4128  evenoddnnnul  4515  funun  5147  enprmaplem3  6079  leconnnc  6219  nchoicelem9  6298  nchoicelem17  6306