Theorem mdandyvrx8

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	mdandyvrx8.1	⊢ ( 𝜑 ⊻ 𝜁 )
	mdandyvrx8.2	⊢ ( 𝜓 ⊻ 𝜎 )
	mdandyvrx8.3	⊢ ( 𝜒 ↔ 𝜑 )
	mdandyvrx8.4	⊢ ( 𝜃 ↔ 𝜑 )
	mdandyvrx8.5	⊢ ( 𝜏 ↔ 𝜑 )
	mdandyvrx8.6	⊢ ( 𝜂 ↔ 𝜓 )
Assertion	mdandyvrx8	⊢ ( ( ( ( 𝜒 ⊻ 𝜁 ) ∧ ( 𝜃 ⊻ 𝜁 ) ) ∧ ( 𝜏 ⊻ 𝜁 ) ) ∧ ( 𝜂 ⊻ 𝜎 ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvrx8.1	⊢ ( 𝜑 ⊻ 𝜁 )
2		mdandyvrx8.2	⊢ ( 𝜓 ⊻ 𝜎 )
3		mdandyvrx8.3	⊢ ( 𝜒 ↔ 𝜑 )
4		mdandyvrx8.4	⊢ ( 𝜃 ↔ 𝜑 )
5		mdandyvrx8.5	⊢ ( 𝜏 ↔ 𝜑 )
6		mdandyvrx8.6	⊢ ( 𝜂 ↔ 𝜓 )
7	2 1 3 4 5 6	mdandyvrx7	⊢ ( ( ( ( 𝜒 ⊻ 𝜁 ) ∧ ( 𝜃 ⊻ 𝜁 ) ) ∧ ( 𝜏 ⊻ 𝜁 ) ) ∧ ( 𝜂 ⊻ 𝜎 ) )