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 ↔ 𝜑 )
	mdandyvrx12.4	⊢ ( 𝜃 ↔ 𝜑 )
	mdandyvrx12.5	⊢ ( 𝜏 ↔ 𝜓 )
	mdandyvrx12.6	⊢ ( 𝜂 ↔ 𝜓 )
Assertion	mdandyvrx12	⊢ ( ( ( ( 𝜒 ⊻ 𝜁 ) ∧ ( 𝜃 ⊻ 𝜁 ) ) ∧ ( 𝜏 ⊻ 𝜎 ) ) ∧ ( 𝜂 ⊻ 𝜎 ) )

Proof

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