Theorem mpanr1 437

Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypotheses

Ref	Expression
mpanr1.1	|- ps
mpanr1.2	|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Assertion

Ref	Expression
mpanr1	|- ( ( ph /\ ch ) -> th )

Proof of Theorem mpanr1

Step	Hyp	Ref	Expression
1		mpanr1.1	. 2 |- ps
2		mpanr1.2	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	anassrs 400	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
4	1, 3	mpanl2 435	1 |- ( ( ph /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  mpanr12  439  axcnre  8161  rec11api  8992  divdiv23apzi  9004  recp1lt1  9138  divgt0i  9149  divge0i  9150  ltreci  9151  lereci  9152  lt2msqi  9153  le2msqi  9154  msq11i  9155  ltdiv23i  9165  ge0gtmnf  10119  sqrt11i  11772  sqrtmuli  11773  sqrtmsq2i  11775  sqrtlei  11776  sqrtlti  11777  cos01gt0  12404