Theorem mdandyvrx12 41160

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
mdandyvrx12.1	⊢ (𝜑 ⊻ 𝜁)
mdandyvrx12.2	⊢ (𝜓 ⊻ 𝜎)
mdandyvrx12.3	⊢ (𝜒 ↔ 𝜑)
mdandyvrx12.4	⊢ (𝜃 ↔ 𝜑)
mdandyvrx12.5	⊢ (𝜏 ↔ 𝜓)
mdandyvrx12.6	⊢ (𝜂 ↔ 𝜓)

Assertion

Ref	Expression
mdandyvrx12	⊢ ((((𝜒 ⊻ 𝜁) ∧ (𝜃 ⊻ 𝜁)) ∧ (𝜏 ⊻ 𝜎)) ∧ (𝜂 ⊻ 𝜎))

Proof of Theorem mdandyvrx12

Step	Hyp	Ref	Expression
1		mdandyvrx12.2	. 2 ⊢ (𝜓 ⊻ 𝜎)
2		mdandyvrx12.1	. 2 ⊢ (𝜑 ⊻ 𝜁)
3		mdandyvrx12.3	. 2 ⊢ (𝜒 ↔ 𝜑)
4		mdandyvrx12.4	. 2 ⊢ (𝜃 ↔ 𝜑)
5		mdandyvrx12.5	. 2 ⊢ (𝜏 ↔ 𝜓)
6		mdandyvrx12.6	. 2 ⊢ (𝜂 ↔ 𝜓)
7	1, 2, 3, 4, 5, 6	mdandyvrx3 41151	1 ⊢ ((((𝜒 ⊻ 𝜁) ∧ (𝜃 ⊻ 𝜁)) ∧ (𝜏 ⊻ 𝜎)) ∧ (𝜂 ⊻ 𝜎))

Syntax hints:   ↔ wb 196   ∧ wa 384   ⊻ wxo 1464

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-xor 1465

This theorem is referenced by: (None)