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