Theorem 2sp 2222

Description: A double specialization (see sp 2219). Another double specialization, closer to PM*11.1, is 2stdpc4 2106. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2219	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2221	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-12 2212

This proof depends on definitions:  df-bi 210  df-ex 1812

This theorem is used by:  cbv1h  2434  csbie2t  3885  copsex2t  5463  fprlem1  8323  frrlem15  9766  fundmpss  36626  bj-cbv1hv  37802  ax11-pm  37838  mbfresfi  38691  cotrintab  44721  pm14.123b  45517  ich2exprop  48660  ichnreuop  48661  ichreuopeq  48662