Theorem mdandyvrx10 48030

Description: Given the exclusivities set in the hypotheses, there exist a proof where ch, th, ta, et exclude ze, si accordingly. (Contributed by Jarvin Udandy, 7-Sep-2016.)

Hypotheses

Ref	Expression
mdandyvrx10.1	⊢ (𝜑 ⊻ 𝜁)
mdandyvrx10.2	⊢ (𝜓 ⊻ 𝜎)
mdandyvrx10.3	⊢ (𝜒 ↔ 𝜑)
mdandyvrx10.4	⊢ (𝜃 ↔ 𝜓)
mdandyvrx10.5	⊢ (𝜏 ↔ 𝜑)
mdandyvrx10.6	⊢ (𝜂 ↔ 𝜓)

Assertion

Ref	Expression
mdandyvrx10	⊢ ((((𝜒 ⊻ 𝜁) ∧ (𝜃 ⊻ 𝜎)) ∧ (𝜏 ⊻ 𝜁)) ∧ (𝜂 ⊻ 𝜎))

Proof of Theorem mdandyvrx10

Step	Hyp	Ref	Expression
1		mdandyvrx10.2	. 2 ⊢ (𝜓 ⊻ 𝜎)
2		mdandyvrx10.1	. 2 ⊢ (𝜑 ⊻ 𝜁)
3		mdandyvrx10.3	. 2 ⊢ (𝜒 ↔ 𝜑)
4		mdandyvrx10.4	. 2 ⊢ (𝜃 ↔ 𝜓)
5		mdandyvrx10.5	. 2 ⊢ (𝜏 ↔ 𝜑)
6		mdandyvrx10.6	. 2 ⊢ (𝜂 ↔ 𝜓)
7	1, 2, 3, 4, 5, 6	mdandyvrx5 48025	1 ⊢ ((((𝜒 ⊻ 𝜁) ∧ (𝜃 ⊻ 𝜎)) ∧ (𝜏 ⊻ 𝜁)) ∧ (𝜂 ⊻ 𝜎))

This proof depends on syntax axioms:   ↔ wb 209   ∧ wa 401   ⊻ wxo 1541

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  df-xor 1542

This theorem is used by: (None)