Theorem 2sp 2185

Description: A double specialization (see sp 2182). Another double specialization, closer to PM*11.1, is 2stdpc4 2075. (Contributed by BJ, 15-Sep-2018.)

Assertion

Ref	Expression
2sp	⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Proof of Theorem 2sp

Step	Hyp	Ref	Expression
1		sp 2182	. 2 ⊢ (∀𝑦𝜑 → 𝜑)
2	1	sps 2184	1 ⊢ (∀𝑥∀𝑦𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2177

This theorem depends on definitions:  df-bi 209  df-ex 1781

This theorem is referenced by:  cbv1h  2425  csbie2t  3923  copsex2t  5385  wfrlem5  7961  fundmpss  33011  fprlem1  33139  frrlem15  33144  bj-cbv1hv  34120  ax11-pm  34157  mbfresfi  34940  cotrintab  39981  pm14.123b  40765  dfich2ai  43621  dfich2bi  43622  ich2exprop  43640  ichnreuop  43641  ichreuopeq  43642