Metamath Proof Explorer

Theorem mdandyvr15

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 mdandyvr15.1 ⊢φ↔ζ
mdandyvr15.2 ⊢ψ↔σ
mdandyvr15.3 ⊢χ↔ψ
mdandyvr15.4 ⊢θ↔ψ
mdandyvr15.5 ⊢τ↔ψ
mdandyvr15.6 ⊢η↔ψ
Assertion mdandyvr15 ⊢χ↔σ∧θ↔σ∧τ↔σ∧η↔σ

Proof

Step Hyp Ref Expression
1 mdandyvr15.1 ⊢φ↔ζ
2 mdandyvr15.2 ⊢ψ↔σ
3 mdandyvr15.3 ⊢χ↔ψ
4 mdandyvr15.4 ⊢θ↔ψ
5 mdandyvr15.5 ⊢τ↔ψ
6 mdandyvr15.6 ⊢η↔ψ
7 2 1 3 4 5 6 mdandyvr0 ⊢χ↔σ∧θ↔σ∧τ↔σ∧η↔σ