Theorem mdandyvrx3

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	mdandyvrx3.1	⊢ ( 𝜑 ⊻ 𝜁 )
	mdandyvrx3.2	⊢ ( 𝜓 ⊻ 𝜎 )
	mdandyvrx3.3	⊢ ( 𝜒 ↔ 𝜓 )
	mdandyvrx3.4	⊢ ( 𝜃 ↔ 𝜓 )
	mdandyvrx3.5	⊢ ( 𝜏 ↔ 𝜑 )
	mdandyvrx3.6	⊢ ( 𝜂 ↔ 𝜑 )
Assertion	mdandyvrx3	⊢ ( ( ( ( 𝜒 ⊻ 𝜎 ) ∧ ( 𝜃 ⊻ 𝜎 ) ) ∧ ( 𝜏 ⊻ 𝜁 ) ) ∧ ( 𝜂 ⊻ 𝜁 ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvrx3.1	⊢ ( 𝜑 ⊻ 𝜁 )
2		mdandyvrx3.2	⊢ ( 𝜓 ⊻ 𝜎 )
3		mdandyvrx3.3	⊢ ( 𝜒 ↔ 𝜓 )
4		mdandyvrx3.4	⊢ ( 𝜃 ↔ 𝜓 )
5		mdandyvrx3.5	⊢ ( 𝜏 ↔ 𝜑 )
6		mdandyvrx3.6	⊢ ( 𝜂 ↔ 𝜑 )
7	2 3	axorbciffatcxorb	⊢ ( 𝜒 ⊻ 𝜎 )
8	2 4	axorbciffatcxorb	⊢ ( 𝜃 ⊻ 𝜎 )
9	7 8	pm3.2i	⊢ ( ( 𝜒 ⊻ 𝜎 ) ∧ ( 𝜃 ⊻ 𝜎 ) )
10	1 5	axorbciffatcxorb	⊢ ( 𝜏 ⊻ 𝜁 )
11	9 10	pm3.2i	⊢ ( ( ( 𝜒 ⊻ 𝜎 ) ∧ ( 𝜃 ⊻ 𝜎 ) ) ∧ ( 𝜏 ⊻ 𝜁 ) )
12	1 6	axorbciffatcxorb	⊢ ( 𝜂 ⊻ 𝜁 )
13	11 12	pm3.2i	⊢ ( ( ( ( 𝜒 ⊻ 𝜎 ) ∧ ( 𝜃 ⊻ 𝜎 ) ) ∧ ( 𝜏 ⊻ 𝜁 ) ) ∧ ( 𝜂 ⊻ 𝜁 ) )