Theorem mdandyvr8

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

	Ref	Expression
Hypotheses	mdandyvr8.1	⊢ ( 𝜑 ↔ 𝜁 )
	mdandyvr8.2	⊢ ( 𝜓 ↔ 𝜎 )
	mdandyvr8.3	⊢ ( 𝜒 ↔ 𝜑 )
	mdandyvr8.4	⊢ ( 𝜃 ↔ 𝜑 )
	mdandyvr8.5	⊢ ( 𝜏 ↔ 𝜑 )
	mdandyvr8.6	⊢ ( 𝜂 ↔ 𝜓 )
Assertion	mdandyvr8	⊢ ( ( ( ( 𝜒 ↔ 𝜁 ) ∧ ( 𝜃 ↔ 𝜁 ) ) ∧ ( 𝜏 ↔ 𝜁 ) ) ∧ ( 𝜂 ↔ 𝜎 ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr8.1	⊢ ( 𝜑 ↔ 𝜁 )
2		mdandyvr8.2	⊢ ( 𝜓 ↔ 𝜎 )
3		mdandyvr8.3	⊢ ( 𝜒 ↔ 𝜑 )
4		mdandyvr8.4	⊢ ( 𝜃 ↔ 𝜑 )
5		mdandyvr8.5	⊢ ( 𝜏 ↔ 𝜑 )
6		mdandyvr8.6	⊢ ( 𝜂 ↔ 𝜓 )
7	2 1 3 4 5 6	mdandyvr7	⊢ ( ( ( ( 𝜒 ↔ 𝜁 ) ∧ ( 𝜃 ↔ 𝜁 ) ) ∧ ( 𝜏 ↔ 𝜁 ) ) ∧ ( 𝜂 ↔ 𝜎 ) )