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