Metamath Proof Explorer

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