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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)))

Colors of variables: wff setvar class

Syntax hints: → wi 4 ∨ wo 357

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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 4127 evenoddnnnul 4514 funun 5146 enprmaplem3 6078 leconnnc 6218 nchoicelem9 6297 nchoicelem17 6305