Metamath Proof Explorer

Theorem mdandyvrx12

Description: Given the exclusivities set in the hypotheses, there exist a proof where ch, th, ta, et exclude ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016)

		Ref	Expression
	Hypotheses	mdandyvrx12.1	$⊢ (φ ⊻ ζ)$
		mdandyvrx12.2	$⊢ (ψ ⊻ σ)$
		mdandyvrx12.3	$⊢ χ \leftrightarrow φ$
		mdandyvrx12.4	$⊢ θ \leftrightarrow φ$
		mdandyvrx12.5	$⊢ τ \leftrightarrow ψ$
		mdandyvrx12.6	$⊢ η \leftrightarrow ψ$
	Assertion	mdandyvrx12	$⊢ ((((χ ⊻ ζ) \land (θ ⊻ ζ)) \land (τ ⊻ σ)) \land (η ⊻ σ))$

Proof

Step	Hyp	Ref	Expression
1		mdandyvrx12.1	$⊢ (φ ⊻ ζ)$
2		mdandyvrx12.2	$⊢ (ψ ⊻ σ)$
3		mdandyvrx12.3	$⊢ χ \leftrightarrow φ$
4		mdandyvrx12.4	$⊢ θ \leftrightarrow φ$
5		mdandyvrx12.5	$⊢ τ \leftrightarrow ψ$
6		mdandyvrx12.6	$⊢ η \leftrightarrow ψ$
7	2 1 3 4 5 6	mdandyvrx3	$⊢ ((((χ ⊻ ζ) \land (θ ⊻ ζ)) \land (τ ⊻ σ)) \land (η ⊻ σ))$