Theorem mdandyvr12

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	mdandyvr12.1	⊢ ( 𝜑 ↔ 𝜁 )
	mdandyvr12.2	⊢ ( 𝜓 ↔ 𝜎 )
	mdandyvr12.3	⊢ ( 𝜒 ↔ 𝜑 )
	mdandyvr12.4	⊢ ( 𝜃 ↔ 𝜑 )
	mdandyvr12.5	⊢ ( 𝜏 ↔ 𝜓 )
	mdandyvr12.6	⊢ ( 𝜂 ↔ 𝜓 )
Assertion	mdandyvr12	⊢ ( ( ( ( 𝜒 ↔ 𝜁 ) ∧ ( 𝜃 ↔ 𝜁 ) ) ∧ ( 𝜏 ↔ 𝜎 ) ) ∧ ( 𝜂 ↔ 𝜎 ) )

Proof

Step	Hyp	Ref	Expression
1		mdandyvr12.1	⊢ ( 𝜑 ↔ 𝜁 )
2		mdandyvr12.2	⊢ ( 𝜓 ↔ 𝜎 )
3		mdandyvr12.3	⊢ ( 𝜒 ↔ 𝜑 )
4		mdandyvr12.4	⊢ ( 𝜃 ↔ 𝜑 )
5		mdandyvr12.5	⊢ ( 𝜏 ↔ 𝜓 )
6		mdandyvr12.6	⊢ ( 𝜂 ↔ 𝜓 )
7	2 1 3 4 5 6	mdandyvr3	⊢ ( ( ( ( 𝜒 ↔ 𝜁 ) ∧ ( 𝜃 ↔ 𝜁 ) ) ∧ ( 𝜏 ↔ 𝜎 ) ) ∧ ( 𝜂 ↔ 𝜎 ) )