Theorem mpjao3danOLD

Description: Obsolete version of mpjao3dan as of 17-Apr-2024. (Contributed by Thierry Arnoux, 13-Apr-2018) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	mpjao3dan.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
	mpjao3dan.2	$$⊢\left(\phi \wedge \theta \right)\to \chi$$
	mpjao3dan.3	$$⊢\left(\phi \wedge \tau \right)\to \chi$$
	mpjao3dan.4	$$⊢\phi \to \left(\psi \vee \theta \vee \tau \right)$$
Assertion	mpjao3danOLD	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		mpjao3dan.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2		mpjao3dan.2	$$⊢\left(\phi \wedge \theta \right)\to \chi$$
3		mpjao3dan.3	$$⊢\left(\phi \wedge \tau \right)\to \chi$$
4		mpjao3dan.4	$$⊢\phi \to \left(\psi \vee \theta \vee \tau \right)$$
5	1 2	jaodan	$$⊢\left(\phi \wedge \left(\psi \vee \theta \right)\right)\to \chi$$
6		df-3or	$$⊢\left(\psi \vee \theta \vee \tau \right)\leftrightarrow \left(\left(\psi \vee \theta \right)\vee \tau \right)$$
7	4 6	sylib	$$⊢\phi \to \left(\left(\psi \vee \theta \right)\vee \tau \right)$$
8	5 3 7	mpjaodan	$$⊢\phi \to \chi$$