Theorem 2sp 2044

Description: A double specialization (see sp 2041). Another double specialization, closer to PM*11.1, is 2stdpc4 2342. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2041	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2043	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-ex 1696

This theorem is referenced by:  cbv1h  2256  csbie2t  3528  copsex2t  4883  wfrlem5  7306  fundmpss  30910  frrlem5  31028  bj-cbv1hv  31917  ax11-pm  32007  mbfresfi  32626  cotrintab  36940  pm14.123b  37649