Theorem mdandyvr11 47968

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.)

Hypotheses

Ref	Expression
mdandyvr11.1	⊢ (𝜑 ↔ 𝜁)
mdandyvr11.2	⊢ (𝜓 ↔ 𝜎)
mdandyvr11.3	⊢ (𝜒 ↔ 𝜓)
mdandyvr11.4	⊢ (𝜃 ↔ 𝜓)
mdandyvr11.5	⊢ (𝜏 ↔ 𝜑)
mdandyvr11.6	⊢ (𝜂 ↔ 𝜓)

Assertion

Ref	Expression
mdandyvr11	⊢ ((((𝜒 ↔ 𝜎) ∧ (𝜃 ↔ 𝜎)) ∧ (𝜏 ↔ 𝜁)) ∧ (𝜂 ↔ 𝜎))

Proof of Theorem mdandyvr11

Step	Hyp	Ref	Expression
1		mdandyvr11.2	. 2 ⊢ (𝜓 ↔ 𝜎)
2		mdandyvr11.1	. 2 ⊢ (𝜑 ↔ 𝜁)
3		mdandyvr11.3	. 2 ⊢ (𝜒 ↔ 𝜓)
4		mdandyvr11.4	. 2 ⊢ (𝜃 ↔ 𝜓)
5		mdandyvr11.5	. 2 ⊢ (𝜏 ↔ 𝜑)
6		mdandyvr11.6	. 2 ⊢ (𝜂 ↔ 𝜓)
7	1, 2, 3, 4, 5, 6	mdandyvr4 47961	1 ⊢ ((((𝜒 ↔ 𝜎) ∧ (𝜃 ↔ 𝜎)) ∧ (𝜏 ↔ 𝜁)) ∧ (𝜂 ↔ 𝜎))

This proof depends on syntax axioms:   ↔ wb 209   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by: (None)