Theorem 19.21bi 1466

Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.21bi.1	⊢ (𝜑 → ∀𝑥𝜓)

Assertion

Ref	Expression
19.21bi	⊢ (𝜑 → 𝜓)

Proof of Theorem 19.21bi

Step	Hyp	Ref	Expression
1		19.21bi.1	. 2 ⊢ (𝜑 → ∀𝑥𝜓)
2		ax-4 1416	. 2 ⊢ (∀𝑥𝜓 → 𝜓)
3	1, 2	syl 14	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1257

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-4 1416

This theorem is referenced by:  19.21bbi  1467  ax11e  1693  eqeq1  2062  eleq2  2117  r19.21bi  2424  elrab3t  2719  ssel  2966  copsex2t  4009  pocl  4067  ordsucim  4253  peano2  4345  funmo  4944  funun  4971  fununi  4994  imain  5008  tfrlem3-2d  5958  findcard  6375  findcard2  6376  findcard2s  6377