Theorem ch2varv 13803

Description: Version of ch2var 13802 with nonfreeness hypotheses replaced with disjoint variable conditions. (Contributed by BJ, 17-Oct-2019.)

Hypotheses

Ref	Expression
ch2varv.maj	⊢ ((𝑥 = 𝑦 ∧ 𝑧 = 𝑡) → (𝜑 ↔ 𝜓))
ch2varv.min	⊢ 𝜑

Assertion

Ref	Expression
ch2varv	⊢ 𝜓

Distinct variable groups:   𝑥,𝑧,𝜓   𝑥,𝑡

Allowed substitution hints:   𝜑(𝑥,𝑦,𝑧,𝑡)   𝜓(𝑦,𝑡)

Proof of Theorem ch2varv

Step	Hyp	Ref	Expression
1		nfv 1521	. 2 ⊢ Ⅎ𝑥𝜓
2		nfv 1521	. 2 ⊢ Ⅎ𝑧𝜓
3		ch2varv.maj	. 2 ⊢ ((𝑥 = 𝑦 ∧ 𝑧 = 𝑡) → (𝜑 ↔ 𝜓))
4		ch2varv.min	. 2 ⊢ 𝜑
5	1, 2, 3, 4	ch2var 13802	1 ⊢ 𝜓

Syntax hints:   → wi 4   ∧ wa 103   ↔ wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by:  sscoll2  14023